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RIVERSIDE TEXTBOOKS 
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fll|||||||H|||l|NIIII|||l |||MlMI|l||IMI||||IMI|||l|HIUI||||IMI||||||il|||l|l|HM|||M<MI|||M>MI|||n<ni|||l|H||||||inU|||IMM||||l|M^ |||| |||ll>'ll|||l>"MmM"S 

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THE 

PSYCHOLOGY OF THE 
COMMON BRANCHES 



BY 



FRANK NUGENT FREEMAN PH.D. 

ASSISTANT PROFESSOR OF EDUCATIONAL PSYCHOLOGY 
THE UNIVERSITY OF CHICAGO 




HOUGHTON MIFFLIN COMPANY 

BOSTON NEW YORK CHICAGO 



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COPYRIGHT, I916, BT FRANK NUGENT FREEMAN 
ALL RIGHTS RESERVED 



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APR I9ISI6 



0)CI,A428G02 



EDITOR'S INTRODUCTION 

The present volume is a very interesting as well as 
a very successful attempt to apply the knowledge 
which we have recently accumulated in the scientific 
applications of psychology to the concrete problems of 
instruction in the elementary school. It is neither a 
scientific treatise on psychology nor a book of special 
methods, though embracing something of the content 
of each. Instead, the present volume occupies a field 
lying between the two, being a presentation of the 
psychological principles underlying the most effective 
instruction in the commonly recognized subjects of 
the elementary-school curriculum. 

Textbooks on general and even applied psychology 
almost of necessity deal with the fundamental prin- 
ciples and generalizations of the science, and the ap- 
plications are usually so remote from the practical 
problems of the teacher that the application to class- 
room procedure is seldom made. On the other hand, 
our books on general and special methods, while often 
very helpful and suggestive in their way, tend never- 
theless to confine their attention to schoolroom de- 
vices and certain general pedagogical principles, and 
do not serve to develop in the teacher any tendency 
to seek out or formulate the reasons for the special 
methods which are being followed. 



vi EDITOR'S INTRODUCTION 

In between these two extremes of psychology on 
the one hand and special or general methods on the 
other lie two new fields in applied psychology — 
genetic psychology, which attempts to organize psy- 
chological knowledge in terms of mental evolution, 
and the psychology of the process of learning to write, 
read, spell, calculate, etc. Genetic psychology lies 
nearer to the pure psychology end, and the psychology 
of learning lies nearer to the methods end. 

The present volume is a treatise on the second of 
these two intermediate fields, namely, the psychology 
of the learning process, and as applied to the so-called 
fundamental subjects of the elementary-school course. 
For three of the subjects applications are made to the 
high-school field as well. The attempt has been made 
so to present the fundamental psychological facts as 
to give a clearer understanding of the pupils' diffi- 
culties, the best methods for overcoming these, and 
the psychological reasons for the special methods to 
be pursued. A leading purpose has been to show the 
teacher how to follow or apply methods intelligently, 
and especially how to adapt methods to the peculiar 
needs of the individual pupil. 

The order of treatment deserves mention, as it 
follows the well-known pedagogical principle of pro- 
ceeding from the simple to the complex. The volume 
begins with the psychology involved in the teaching 
of handwriting, which requires a relatively simple 
form of learning of the sensori-motor type. This is 



EDITOR'S INTRODUCTION vii 

followed by the psychology involved in teaching 
drawing, reading, and music, which are good examples 
of what is known as "perceptual" learning. Next 
follows the psychology of instruction in spelling, which 
is an example of the fixing of associations. This in 
turn is followed by history and geography, which are 
examples of a more difficult teaching process, as they 
involve the organization and extension of experience 
through the use of the imagination. Next comes the 
psychology of teaching mathematics, with applica- 
tions to instruction in algebra and geometry as well 
as arithmetic, studies which involve abstract thinking. 
The volume closes with a consideration of the psycho- 
logical principles involved in giving instruction in the 
natural sciences, which involve the ability to general- 
ize upon the basis of accumulated experience. Taken 
in this order and together, the different elementary- 
school subjects offer an excellent basis for the presen- 
tation of the chief types of the learning process. 

Such a volume as this would not have been possible 
a decade ago, and the fact that it is possible to-day 
serves to illustrate the rapid advances being made in 
experimental education. It has required much tech- 
nical knowledge and considerable skill in presentation 
to organize, in a simple and non-technical form, the 
practical results of the many scientific studies of the 
learning process which have so far been made. As a 
textbook in courses in elementary education in normal 
schools and colleges this volume should find large 



viii EDITOR'S INTRODUCTION 

usefulness, and it should also prove of much service 
as a simple treatise on the psychology of elementary- 
school methods for teachers organized into reading 
circles or study clubs. 

Ellwood p. Cubberlet. 



PREFACE 

During recent years there has been a good deal of 
investigation for the purpose of analyzing the learning 
processes which are characteristic of the common 
branches. The publication of E. B. Huey's Psychology 
and Pedagogy of Reading marked the first attempt to 
bring together some of this material and present it in 
such a form that it would be serviceable to teachers. 
Additional material on reading has become available, 
and considerable work has also been done on writing 
and spelling, and a little on number. The accumulation 
of data has reached a point which seems to justify a 
comprehensive account of the psychology of the com- 
mon branches. The amount of experimental founda- 
tion for the analysis of the different subjects varies 
from a fairly satisfactory amount down to nothing. 
In the case of the subjects which have not been directly 
investigated, however, there has been experimentation 
upon the mental processes which are very obviously 
involved in them — as in the case of history — so that 
most of the discussion has some experimental founda- 
tion, direct or indirect. No apology is made for the 
fact that a part of the analysis is in the nature of infer- 
ence from general principles which have been thus 
determined, beyond the acknowledgment that such 
analysis is subject to later verification or revision by 



X PREFACE 

direct experimentation. One benefit to be derived 
from making a formulation, when experimentation is 
not yet complete, is that this serves to define some of 
the problems and thus to stimulate investigation. 

I take pleasure in using this opportunity to make 
certain general and specific acknowledgments. For 
the early direction and the continued encouragement 
in the pursuit of psychology I am indebted to my col- 
lege teachers, Professors A. C. Armstrong and Ray- 
mond Dodge. Both in my work as a graduate student 
and as an instructor I have been closely associated 
with Professor Charles H. Judd, and owe the special 
direction of my efforts, and much of the formation of 
my views, to his influence. He has also given helpful 
criticism upon the manuscript of this book. Professor 
S. C. Parker has given me valuable criticism and stim- 
ulus, and I am indebted to Professor W. L. Miller for 
carefully reading the whole manuscript. To many 
others I am indebted, either for their general influence 
and stimulus or for suggestions concerning the manu- 
script. The help of all these, whether mentioned by 
name or not, I gratefully acknowledge. 

F. N. F. 

Chicago, March 1, 1916. 



CONTENTS 

I. Introduction 1 

II. Handwriting: Learning chiefly of a Sensori- 
motor Character 6 

The composition and development of the writing 

habit. 
Modifications due to age. 
Individual differences and practice periods. 

III. Drawing: Perceptual Learning .... 34 

A demonstration experiment in drawing. 

The nature of perception as illustrated in drawing. 

Development of drawing with age. 

General account of the nature of perception. 

The value of sense training. 

IV. Reading: Perceptual Learning .... 67 

The relation of reading, writing, and spoken language. 
The stages in learning to read. 
Oral and silent reading. 
EflBciency in reading. 

V. Music: Perceptual Learning 98 

The recognition of intervals and melody. 

Rhythm. 

Harmony. 

Tone-quality. 

VI. Spelling: Fixing of Associations . . . .115 

The associations in spelling. 
Methods of learning to spell. 
The principles of the drill method. 



xii CONTENTS 

VII. History: Extension of Experience through 

Imagination 132 

General account of imagination. 

The types of imagination employed in history. 

The historical sense. 

The grasp of historical development. 

Critical examination of sources. 

VIII. Geography: Extension of Experience 

THROUGH Imagination 161 

Growth of spatial imagination or orientation. 
Maps and globes. 

IX. Mathematics: Abstract Thought . . . 179 
Number an abstract mental process. 
The early development of the number idea. 
The development of the arithmetical operations. 
The mental processes in algebra. 
The development of geometry from measurement. 

X. Natural Science: Generalization upon Ex- 
perience 239 

Concept formation. 

The development of generalization. 

The practical and theoretical in science teaching. 

Questions and Topics for Discussion . . 265 
Index 273 



THE PSYCHOLOGY OF THE 
COMMON BRANCHES 

CHAPTER I 

INTRODUCTION 

When the child takes pencil and paper and makes 
his first attempt to write, he is beginning a long course 
of training in the particular form of learning which we 
call " sensori-motor." His first attempt is to make a 
mark which shall look like the marks which are set be- 
fore him as a copy, and the progress which he makes 
as he practices consists in getting better and better 
control over his movements so as to be able to pro- 
duce letters and words which look more and more like 
the copy. Writing does not require in any large degree 
the exercise of memory, of imagination, or of reason- 
ing. It requires, as the term " sensori-motor " implies, 
the adaptation of movements to an object which is 
perceived. In learning to read, on the other hand, 
movements play a minor part compared with the ac- 
quirement of the ability to recognize quickly and cor- 
rectly the combinations of letters as they appear in 
words, and to give them their true meaning. The un- 
derstanding of number requires that one shall dis- 
regard most of the qualities of objects and pay atten- 



2 PSYCHOLOGY OF COMMON BRANCHES 

tion only to their number. Accordingly, we say that 
learning number involves the process of abstraction. 
Similarly, other subjects of the curriculum furnish il- 
lustrations of other forms of learning. 

There is a great deal of variation in the efficiency 
with which these various kinds of learning are carried 
on in the school. Some children learn rapidly, others 
slowly. Some waste effort, others economize it. Some 
reach a high degree of proficiency, others remain per- 
manently at a low level. If we compare, not individual 
children, but different classes or schools or school sys- 
tems doing the same work, large differences in efficiency 
still appear. 

A certain proportion of the differences between 
individual children, and even between different classes 
or schools, may be attributed to differences in native 
ability, but in large measure a child learns economically 
and well, or the reverse, according as his learning is 
supervised well or poorly. The child may stumble 
along and by blind trial learn how to improve. In some 
forms of learning, in fact, random trial forms a fairly 
large part of the method. But when the child's efforts 
are not intelligently guided, the amount of blind trial 
is larger than necessary, and much time is wasted in 
consequence. Experiments in supervised study have 
shown that, even in the high school, the pupil needs 
considerable help from the teacher to show him how to 
go about his work in its more general aspects, and to 
meet the special difficulties of each subject. How much 



INTRODUCTION 3 

more is the elementary-school pupil in need of skilled 
supervision ! 

In order to supervise the child's learning most 
effectively, it is necessary to know what mental 
changes take place in the different forms of learning 
which he undertakes. Merely to know the result which 
is aimed at is not sufficient — important as this is. 
One can learn in a short time to distinguish between 
good and poor writing, between an adequate and an 
inadequate understanding of history or geography, or 
between different degrees of proficiency in the pursuit 
of a science. A clerk can correct examination papers 
in arithmetic or spelling. These forms of discrimina- 
tion make up the art of the examiner. When carried to 
a high degree of perfection in the development of 
standard tests of attainment, this art becomes more 
difficult, and it becomes possible to use the results in 
directing the pupil's efforts. But in the main the art of 
the teacher is the far more delicate one of following 
the changes which take place in the mind of the pupil, 
and of bringing to bear his influence upon them to 
produce the highest degree of improvement with the 
least expenditure of effort. In order to understand the 
process which is going on in the child's mind when he 
learns the various branches, it is necessary to have a 
conception of the typical learning processes which are 
involved in these branches. 

It might be supposed that, having gone through the 
learning processes himself as a child, the teacher would 



4 PSYCHOLOGY OF COMMON BRANCHES 

have sufficient insight into their nature from his mem- 
ory of his own eflForts, without making any further 
study of them. This memory of one's early struggles, 
however, is not sufficient. In the first place, memory has 
become very dim with time. From great familiarity 
with the tasks which the child has to meet, one becomes 
subject to the illusion that they are easy, and that the 
only requisite for their performance is good-will. Let 
the teacher try one or two of the tasks which are sug- 
gested in the following pages as illustrations of learn- 
ing of a sensori-motor or a perceptual sort, — such as 
writing with the left hand or the toes, or gaining a 
correct apprehension of the figure shown in chapter III, 
— and he will get something of the baffled, helpless 
feeling which possesses the child which will set him to 
searching for some way to help the child to find out 
how to meet the demands which are laid upon him. 

A second reason why the teacher's early experience 
is not enough to fit him for the task of guiding the 
child in his learning is that the learning attitude and 
the teaching attitude are different. The learner is 
absorbed mainly in the result which he wishes to 
accomplish, and he does not make much analysis of 
the means by which he reaches his goal. In fact, he 
sometimes will reach his goal more quickly if he does 
not analyze the process very much. But the teacher 
must have the analytical attitude. He must be con- 
tinually thinking about how the act which he is teach- 
ing can best be performed. For example, the child in 



INTRODUCTION B 

writing does not pay attention to the movement so as 
to know what simple movements compose it and how 
they work together, but this information helps the 
teacher to give the child exercises which will emphasize 
the proper components. 

While the analysis of the learning process in the 
common branches, which occupies the following chap- 
ters, does not go into the details of the methods of 
teaching, the constant aim is to give practical assist- 
ance to the teacher by giving the basis for an intelli- 
gent use of methods. The different school subjects 
taken together furnish a pretty comprehensive set of 
examples of the various kinds of learning of which the 
human mind is capable. The subjects are so arranged 
that the simpler, more elementary, and less intellectual 
forms of learning come jfirst, and the higher types in 
their order. The topics taken together furnish a fairly 
complete account of psychology in its active or funo 
tional aspect, apart from the instincts and emotions. 



CHAPTER II 

HANDWRITING: LEARNING CHIEFLY OF A 
SENSORI-MOTOR CHARACTER 

The sensori-motor form of learning of which hand- 
writing is an example has for its purpose the develop- 
ment of a motor habit/ A motor habit exists when 
such a connection has been formed between a set of 
stimuli ^ and the movements which are made in re- 
sponse to them, that the movements follow readily 
upon the stimulus without the necessity of being guided 
and directed in detail. Thus, when a person wishes to 
write a word, it is not necessary to think about the 
movements of the fingers or the arm which produce 
the letters, nor is it necessary to think of the details of 
the letters themselves. This is true of all sorts of 
sensori-motor habits. 

The composition and development of the writing habit 

The problems of teaching writing are concerned very 
largely with the development of an efficient movement. 
We may, then, turn first to a consideration of the com- 

^ A sensori-motor activity is one which consists in the adaptation 
of a movement to a stimulus. 

* A stimulus is any object or event in the world outside the indi- 
vidual which is capable of causing a sensation, an idea, or a move- 
ment — or, in other words, of producing a response. 



HANDWRITING 7 

position of the writing movement and of the way in 
which it is developed. 

The writing movement is a very complex one. It is 
composed of a great many elementary or simple move- 
ments. In the first place, there is the movement of the 
fingers and of the hand. Even if the letters are not 
formed by finger movements, the fingers must be 
employed in holding the pen. In doing this the first 
and second fingers are separated in their action from 
the third and fourth. The first two fingers with the 
thumb hold the pen, while the third and fourth fin- 
gers support the weight of the hand. This division 
among the fingers is something which is more or less 
artificial; that is, it is not the natural manner in which 
the child grasps objects. The most primitive method 
of grasping an object, which is seen not merely in the 
child but also in the monkey, is to fold the four fingers 
about it without using the thumb. The ability to 
place the thumb against the tips of the fingers in 
grasping an object is a distinctly human one and one 
which develops later in the child than the other form. 
The mere act of holding the pen in the conventional 
manner, then, is a matter of considerable difficulty to 
the child. 

In addition to the adjustments or the movements of 
the fingers there are movements of the various arm 
joints. The wrist is frequently moved from side to side 
during the writing of the letters of a word. This is not 
a movement which is commonly approved by writing- 



8 PSYCHOLOGY OF COMMON BRANCHES 

masters, but it is very generally used. The hand also 
is carried along the line by the movement of the elbow 
and of the shoulder, together with the wrist. Whether 
the greater part of the movement is made at the elbow 
joint or at the shoulder will depend on the height to 
which the arm is raised. If the arm hangs at the side, 
none of the movement is made at the elbow. The 
movement by which the letters are formed may also 
be made partly at the shoulder joint. This movement 
is sometimes called the forearm movement, but it is 
not, as a matter of fact, made by the forearm. It may 
be made with the arm resting on the muscle pad of the 
forearm, but the muscles which produce the movement 
are at the shoulder. The muscles in the forearm, on 
the contrary, control the movements of the fingers, as 
may be readily verified by placing the other hand on 
the forearm and then closing the fingers. 

These component movements cooperate in the total 
movement. The writing movement to be most efficient 
should be made up of a combination of these various 
component movements, since each of them is particu- 
larly suited to carry on some part of the whole task. 
The side-to-side movement of the forearm, revolving 
about the muscle pad as a center, should carry the 
hand along from the left to the right side of the paper; 
and this movement should go on while the letters are 
being formed so that the writing does not have to be 
interrupted. The movement of the whole arm from 
the shoulder resting on the muscle pad of the forearm 



HANDWRITING 9 

is well suited to carry the hand up and down so as to 
play the chief part in making the upward and down- 
ward strokes. It is probable that this large movement 
produces a rhythm and regularity in the writing and a 
smoothness of stroke which gives the written page a 
good appearance. 

Furthermore, it is probable that if a considerable 
part of the movement is made with the arm, it is not 
so fatiguing as when the fingers do the whole work. 
The finer parts of the letters can most easily be made 
with the fingers. Although the attempt is commonly 
made entirely to exclude finger movement, it rarely 
succeeds, and the most rational course is to recognize 
that the fingers, as well as the arm, have their own 
part to play. 

Overslant at the end of the line may be corrected by 
pronation. Besides these components of the writing 
movement which produce the words, there is one which 
is sometimes used to correct a fault resulting from the 
mechanical conditions of writing. As the hand is 
moved forward by the rotation of the forearm about 
the muscle pad or the elbow as a center, the pen points 
more and more to the right. This is illustrated in 
Figure 1. This causes, unless it is corrected, an over- 
slant of the writing at the right end of the line. In 
order to correct this overslant, some writers turn the 
hand and wrist over to the left, as it moves along the 
line, so that the palm is more turned-down or prone 
and the penholder is more nearly vertical. This move- 



10 PSYCHOLOGY OF COMMON BRANCHES 

ment is called " pronation." The reader may experi- 
ment by comparing one series of strokes made while 
the palm is prone and another in which the hand is 
turned over toward the right, and he will see that those 




Fig, 1. CHANGE IN SLANT DUE TO THE MOVEMENT OF THE 
HAND ALONG THE LINE 

made with the hand turned down are more nearly ver- 
tical than the others. Turning the hand down in pro- 
nation, therefore, tends to correct the overslant of the 
writing at the end of the line. 

There are also adjustments of the eyes and of the 
body. It will thus be seen that all the chief parts of 
the hand and arm are used in writing, but this does not 
exhaust the list of movements which are made or of 
adjustments which must be maintained. The eye 
moves in order to follow the writing of the letters and 
to guide the movement. This must not be regarded as 



HANDWRITING 11 

an unimportant part of the whole activity. It is so 
important that it has been largely due to the recogni- 
tion of the eye movements that important changes in 
the teaching of writing have been made. In order that 
the arm may be free to move and may have a solid 
support, the body must be held in position. The posi- 
tion which is taken will have an important effect upon 
the ease and fluency of the movement. This also has 
an important bearing upon the practical determination 
of the type of writing which ought to be taught. 

Health demands good posture. The correct posture 
in writing is also determined by the demands of health. 
In order that the eyes shall not be subjected to strain, 
the writer must face the desk squarely and the paper 
must be near the middle line of the body so as to bring 
the two eyes the same distance from the writing. In 
order that the spine shall not be twisted and bent to 
the side, both arms should rest on the desk. In order 
that the lungs, stomach, and other vital organs shall 
have sufficient room, the body should be erect. 

The application of correct posture to the position of 
arm and paper. It was formerly thought that these 
conditions necessitated vertical writing. Such is not 
the case, but it is necessary that the body or the head 
should not be turned or twisted. The paper may be 
tilted about thirty degrees to the left so that the line 
on the page is about at right angles to the line of the 
forearm. This will enable the arm to carry the hand 
along the line. The writing will then naturally have 



12 PSYCHOLOGY OF COMMON BRANCHES 



a slant from the perpendicular by about the amount 
to which the paper is tilted, as is shown in Figure 2. 
This is based upon the fact that the upward and down- 
ward strokes of the 
writing naturally fall 
approximately in the 
direction perpendicu- 
lar to the edge of the 
desk. Writing which 
has an angle of sixty 
to seventy degrees to 
the base-line is, then, 
the best suited to 
meet the require- 
ments for an easy 
movement and at the 
same time to satisfy 
the demands of hy- 
giene. More particu- 
lar specifications of method must be left to discussions 
of the teaching of writing. 

The first process in motor learning is the selection 
of the appropriate movements. When the child first 
attempts to write, he is deficient in that he is not able 
to select just the movements which will be appropriate 
to produce the desired result. The first point, then, 
concerns the selection of the appropriate movements. 
The child by the time he begins to learn to write has 
sufficient general control over his bodily activities so 




Fig. 2. DIAGRAM OF THE RELATION 
OF THE BODY AND ARMS TO THE 
DESK AND THE PAPER 



HANDWRITING 13 

that he can in a general way call into action the groups 
of muscles which are to be used in such an act as 
writing. If he sees somebody else write, he can imi- 
tate very roughly the manner of holding the pen and of 
making the movements. But his attempt does not re- 
sult in the contraction of just the muscles which pro- 
duced particular strokes. Many useless movements 
are made. It may be seen from the observation of the 
child in the earlier stages of his learning that this ex- 
tension to unnecessary movements is widespread. He 
contracts the muscles of the face, twists the body into 
unnatural positions, perhaps clenches the left hand, 
and presents the spectacle of general muscular tension. 
This preliminary stage in the development of move- 
ment is called "diffusion." The nervous energy has as 
yet no well-connected channels of discharge, and there- 
fore scatters over a large area of the nervous system. 
Learning consists, then, in the first place, in confining 
the nervous energy, so far as possible, to the particular 
muscles which are needed to produce the effect. 

Selection means also inhibition. This selection of 
the appropriate movements or the reduction of diffu- 
sion involves the inhibition ^ or the prevention of the 
contrary movements. There are two possible methods 
of attempting this selection. We may think particu- 

^ Inhibition means the checking or prevention of any activity, 
whether movement or train of thought. Thus the thought of the 
coldness of the water may inhibit the impulse to jump in, or the 
contraction of the muscles which raise the foot in walking inhibit 
the contraction of the muscles which extend it. 



14 PSYCHOLOGY OF COMMON BRANCHES 

larly of the movement which is to be made or we may 
fix our mind upon the movements which are to be 
inhibited. In some cases, it is not well to think of the 
movements at all, but only of the result which is to be 
obtained by them, in this case the formation of the 
letters on the paper. Whichever object is in the atten- 
tion, the same principle holds. This principle is that 
it is better to fix the attention upon the movements 
which are to be made or upon the result which is 
desired, rather than upon the movements which are to 
be eliminated or the result which is not desired. A 
stock illustration of this principle may be taken from 
learning to ride a bicycle. When a person thinks of the 
obstruction in the road or of the ditch at the side, he is 
very likely to run into the obstruction or fall into the 
ditch. His salvation consists in keeping his mind fixed 
upon the path along which he wishes to travel. 

Application. The application of this principle to 
writing is that the child should not be made anxious 
concerning the useless or superfluous movements 
which he makes. In its application to the form of the 
letters, he should be thinking chiefly of the form which 
he wishes to produce rather than of those forms which 
he wishes to avoid. It is, of course, necessary for him 
to examine his own writing so that he may detect the 
faults in it in contrast with the correctly formed letters. 
He is apt, if this is not done, to fail entirely to see the 
faults in his writing; but after the fault has been 
detected, his attention is then to be fixed on the cor- 



HANDWRITING 15 

rect form which is to be substituted for the incorrect 
one. 

Along with the selection of the appropriate move- 
ments goes the organization of these separate move- 
ments into the total or combined movements. This 
building together of movements is called " coordina- 
tion." ^ In a coordination the movements must be 
adjusted to one another in such a way that each one 
is made with the proper amount of force. The failure 
to have them properly adjusted may be seen from the 
results of an experiment in which the pressure exerted 
by the thumb and the two fingers was measured. It 
was found that in a straight downward stroke the 
index finger, as one should expect, exerts the chief 
pressure, while the second finger and the thumb guide 
the movement. If, now, the downward stroke curves 
to the left, it is because the middle finger exerts an 
undue amount of pressure. If each finger does not 
exert its due or proportional amount of force in making 
any particular line, the stroke is thrown out of its 
correct course. 

The successive movements must also follow one 
another in the proper time. The smoothness and ease 
of movement will depend very largely upon whether 
or not the successive parts thus follow one another as 
they should. There are certain gymnastic feats, for 

* A motor coordination is a group of simple movements which 
combine simultaneously or successively to produce some definite 
result. 



16 PSYCHOLOGY OF COMMON BRANCHES 

example, which are not difficult, provided one makes 
the movement or exerts the effort at the proper time, 
but which are impossible if this is not done. A simple 
illustration of the failure to time the writing move- 
ments correctly is taken from the relationship of the 
movements of the arm in carrying the hand across the 
page and the movements of the fingers in forming the 
letters. Some writers alternate these two movements. 
They use the fingers extensively in the formation of 
several letters and then interrupt the finger movement 
to lift the hand and carry it forward. A much better 
relationship is maintained between these movements 
by performing them simultaneously. 

Rhjrthm is an important aid in timing the movements, 
The best means of bringing about the correct timing 
of the component movements of a coordination is to 
make the whole movement rhythmical. When the 
movement is carried on so that certain prominent 
strokes are made at regular intervals of time, as in 
marching to music, all of the elements of the move- 
ment are apt to fall into place at the proper time and 
with the proper force. This principle is used in writing 
when a class writes to count or to music It has been 
found by experiment that the use of rhythm which 
is suited to the age and training of the pupils increases 
the speed and improves the quality of their writing. 
If too rapid a rate is used, the quality becomes poorer. 
Not all the children of a class can profitably use the 
rate which is suited to the majority and a few are 



HANDWRITING 17 

deficient in the sense of rhythm, but if due provision is 
made for the exceptional cases the use of rhythm is a 
valuable means of teaching writing, or in fact any form 
of motor coordination. 

A movement is learned through repetition. The 
method by which the coordination is formed through 
the selection of movements and their organization is 
the frequent repetition of trials. The coordination can- 
not be formed by telling the pupil how the movement 
is made. It is necessary that he find out for himself 
through making an attempt, noting the results of 
his attempt, and then endeavoring to improve his 
movement so as to retain these results which are the 
ones aimed at and eliminate those which are not the 
ones desired. This method of learning is sometimes 
called the " trial-and-error " method and sometimes 
the " trial-and-success " method,^ according as we are 
thinking of the elimination of the wrong trials or the 
retaining of the correct ones. The fact cannot be too 
strongly emphasized that the only method by which 
such a form of learning can succeed is through practice. 
The child may be assisted in taking the correct posi- 
tion by being instructed, or being shown how, and his 
attention may be directed toward his mistakes. In a 
variety of ways verbal instruction as to how the move- 

* The trial-and-error, or trial-and-success, method of learning is 
one in which one learns to make an adjustment, not by studying the 
problem which is presented, but by attacking it more or less blindly 
and then gradually eliminating the unsuccessful, and retaining the 
successful trials. 



18 PSYCHOLOGY OF COMMON BRANCHES 

ment should be made is of great value to the learner, 
but it only supplements the trials which he makes and 
can never be a substitute for them. Moreover, it is 
necessary that frequent trials be made. The mistake is 
sometimes made, though not so often as formerly, of 
requiring the pupil to make a few copies only at each 
practice period and to make each one slowly and labo- 
riously. A much better method is to require him to 
make a large number of copies somewhat more fluently, 
endeavoring to improve in each case over his preceding 
trial. 

As learning progresses, attention is freed from the 
details of the movement. As the child learns better to 
coordinate the movements, a change takes place in his 
mental attitude toward his bodily response. At the 
beginning it was necessary to think of each separate 
movement and each stage in the making of a letter. 
As he becomes more skilled, he is able to make a series 
of movements or to form a letter or a word, thinking 
only of the whole group of movements or of strokes. 
The recognition of the movement becomes simplified 
and the details are given over to the control of the 
nervous centers which produce the movement. When 
this simplification of the recognition is carried far 
enough, we reach the automatic stage of the habit. 
This means that the attention is turned to the thought 
which is being expressed. 

Increased skill makes possible the development of 
rhythm. As the child's attention becomes freed from 



HANDWRITING 19 

the details of the movements or of the letters, he is 
able to recognize more fully some of the more general 
features of the writing. One of these general features 
which has already been mentioned is rhythm. The 
child can write rhythmically only when he does not 
have to stop to consider how to form the details of the 
letters or to adjust his hand or jBngers. Rhythm ap- 
pears when the successive strokes are made in about 
the same time. Measurements have shown that this 
is true of the writing of the older child or the adult, 
even though the successive strokes differ greatly in 
length. The age at which the writing becomes thus 
markedly rhythmical in the case of the majority of 
children is nine or ten. We may conclude from this 
fact that this is the age at which it is suitable to give 
the child writing drills which require a high degree of 
rhythm. 

Changes in speed within the letter are more deter- 
mined by the mechanical ease or difficulty in adult 
than in children's writing. Another significant fact 
which has been discovered by experiment and which 
indicates that the child's attention is being withdrawn 
from the details of the letters is that in the writing of 
the older child and the adult the speed varies much 
more in the different parts of the letter than in the 
writing of the younger child. Where the mechanical 
difficulties are considerable, as where there is an 
abrupt change in direction, the movement continues 
to be relatively slow, while where the mechanical diffi- 



20 PSYCHOLOGY OF COMMON BRANCHES 

culties are slight, as on a long, sweeping stroke, the 
speed increases. 

Attention can be given to uniformity. Another gen- 
eral feature of the writing besides rhythm to which 
the child can give attention after the details cease to 
trouble him is the uniformity of the words and letters. 
This includes uniformity of slant, of alinement or of 
spacing. Young children commonly form their letters 
carefully, but their writing presents an uneven appear- 
ance. 

The writing habit includes word and letter recogni- 
tion as well as movement. We are accustomed to 
think of such a habit as writing as being composed of 
movements. This is true, but movements are not all 
there is to the habit. The movements are made in 
response to the sight of letters and words. At the very 
beginning the writer looks at the letters and copies 
them, thus holding the form of the letters in mind for 
only a short time. Later on, the letters need not be 
seen, but must be present in imagination. Later still, 
the form of the letters may largely drop out of mind, 
but even in this most advanced stage the thought of 
the word exists in the mind and is the stimulus to the 
movement. In the case of writing, then, we may sepa- 
rate two phases of habit, that of the movement and 
of the recognition of the stimulus. 

Writing stimulates a study of letter forms. It is 
appropriate to say in this connection that the writing 
habit, considered as a form of movement, is of import- 



HANDWRITING 21 

ance in the development of the recognition of the let- 
ters. Before the child begins to write, it is necessary 
that he shall be able to distinguish the forms of the 
different letters roughly. He may, however, distin- 
guish them sufficiently for reading, but not for writing. 
As he tries to reproduce the forms which he perceives, 
he finds it necessary to pay more attention to the form 
than he has previously done. Writing furnishes a 
stimulus to a further study of the form of the letters. 
Writing also furnishes an additional experience 
which enriches the perception of form. After a person 
has learned to write letters, his recognition of them is 
not merely a matter of sight. There is a tendency, 
when the letters are seen, to make the movement of 
producing them. There are numerous illustrations 
from our mental life which show that our recognition 
of objects includes the experience which we have had 
in handling them. If we lift two boxes which are the 
same in weight, but of different size, we are subject to 
an illusion. The smaller box appears to be much heav- 
ier than the large one. This is because in looking at 
the boxes the sensation of sight produces an anticipa- 
tory contraction of the muscles which would be used 
in lifting the boxes. When, now, we do lift them, there 
is a strong contrast between the amount of force 
which is exerted in the case of the two hands, because 
we had anticipated the necessity of lifting the larger 
box more vigorously. This contrast causes the feeling 
of greater strain in lifting the small box which makes 



22 PSYCHOLOGY OF COMMON BRANCHES 

it appear heavier than the larger one. So also in our 
recognition of letter forms there is included something 
of the motor experience of making them. 

The writing movement becomes the means of ex- 
pressing meanings. We have been discussing writing 
as a form of movement which becomes organized so 
that it becomes an effective means of producing the 
forms of letters and words on paper. The true function 
of writing is fulfilled when, in addition to this, it 
becomes the expression of meanings. Meanings are 
represented first in spoken words, and when we write 
we commonly say over and hear inwardly the words. 
Because meaning was originally associated with the 
spoken and heard word, it is still embodied in internal 
speaking and hearing. When writing advances to the 
stage at which it is a ready means of expressing mean- 
ings, it is carried on as a direct response to ideas em- 
bodied in these forms. The consciousness of the move- 
ments or of the details of the form of the letters recedes 
to the background. When this stage is reached writing 
has become automatic. 

The habit may become automatic too soon. In the 

development of writing toward this automatic ^ stage, 

there may be two opposite faults. The habit may 

become automatic at a stage when it is not sufficiently 

well developed; that is, the person may learn to express 

his thoughts through a form of movement which is 

^ An activity is automatic when it is carried on with little or no 
attention to the activity itself. Thus one may take a key from his 
pocket and unlock a door automatically. 



HANDWRITING 23 

irregular and which produces illegible letters. The 
cure of this fault is to give attention to the habit until 
it becomes developed to the point at which the results 
of the writing are satisfactory. The results may be 
unsatisfactory either because the movement is awk- 
ward or because the writing is poor in quality. 

Attention may be given to the details too long. The 
opposite fault also sometimes occurs. In this case a 
person never loses his consciousness of the writing 
movement or of the form of the letters which he is 
producing sufficiently to give his attention wholly or 
chiefly to the thought. Persons sometimes possess two 
styles of writing, one in which the habit is automatic 
and the writing is very poor, and another in which the 
writing is kept at a high grade through giving attention 
to it. This development of two sorts of habit, one which 
is used in the ready expression of thought and the 
other in producing pleasing forms, is unfortunate. The 
child should develop his writing habit to a sufficient 
degree of perfection that he may produce good results, 
but it should then become automatic. 

Movement and form both require attention. Differ- 
ent systems of teaching give different emphasis to the 
development of a good motor coordination as com- 
pared with the production of writing which presents 
a good appearance. Some teachers believe that if care 
is taken to develop good movement the form will take 
care of itself, or at least will not need much atten- 
tion. It is true that writing is to be thought of as a 



24 PSYCHOLOGY OF COMMON BRANCHES 

movement habit, and that the principles which govern 
its development as a movement are those which must 
guide the teacher in the methods which he uses, as we 
have already seen in detail. But a movement is made 
in response to a stimulus, and it is to be judged by 
the accuracy with which it is adjusted to the stimulus. 
A movement is not judged merely according to its ease 
or smoothness. The handwriting movement, accord- 
ingly, may be smooth and easy, and yet the writing 
may not be legible because the letters are poorly 
formed or not well spaced. 

The child should study form. There are effective 
and ineffective ways of calling the child's attention to 
the form of the letters which he is producing. One 
method is merely to place a model before him and 
require him to copy it. This method, if used alone, is 
seriously deficient in two ways. In the first place, it 
gives the child merely the finished product, and, if the 
copy is engraved, a finished product that he could not 
possibly imitate. In place of this copy he should have 
an opportunity to see the form being produced. The 
form does not in itself suggest the best method of 
reproducing it. The form must be recognized by the 
child in terms of the movement of producing it. In the 
second place, merely to set before the child a perfect 
model does not enable him to see just in what respect 
his writing differs from it. To gain this end it is neces- 
sary to show him how to make an analysis of the form 
of his writing. 



HANDWRITING 25 

Fonn should be analyzed. One means by which the 
child may be helped to make such an analysis is to 
show him series of charts in which progressive degrees 
of excellence in each of the main elements of form are 
illustrated.^ For example, one series of charts may 
show different degrees of uniformity in slant or aUne- 
ment, another different qualities of line or stroke, 
another different degrees of excellence in letter forma- 
tion, and another degrees of excellence in spacing. By 
the study of such charts and an analysis of his own 
writing the child may gain a clearer recognition of the 
ways in which his writing deviates from the model. 

The child can be guided in the development of the 
best movement. If some teachers emphasize move- 
ment to the neglect of form, others commit the oppo- 
site error. It is clear from the whole trend of our dis- 
cussion why this is a mistake. It is a far safer and more 
economical method to guide the child in the formation 
of those habits of movement which experience has 
shown to be the most efficient than to allow him to 
blunder into a form of movement without any assist- 
ance. Substantially the same form may be produced 
in a variety of ways, and some of these are much bet- 
ter than others. It is the business of the teacher to 
help the child to find these better ways as rapidly as 
possible. 

^ Such a series is published in the appendix of The Teaching of 
Handwriting, by the author, published by Houghton Mifflin Com- 
pany (1914). 



26 PSYCHOLOGY OF COMMON BRANCHES 

The elements which can be acquired through 
instruction constitute good form. It has been said in 
a former paragraph that the writing movement could 
not be learned through instruction, but must be devel- 
oped through the trial and success method. This 
applies to what may be called the execution of the 
movement. There are certain aspects of the movement, 
on the other hand, which may be partly learned throilgh 
imitation or through instruction. The child may gain 
help through these methods in learning how to hold 
the pen, what position should be assumed by the hand 
and arm, and in a general way what parts to move in 
making the strokes. These aspects of the activity may 
be called " form." Form, in this sense, is, of course, 
entirely different from the form of the letters or the 
words. We use the term in the same sense as when we 
speak of good form in playing tennis or performing a 
gymnastic feat or riding a horse. There are elements 
of good form in writing which there is not space to 
enumerate here. A general idea of what they are may 
be gained from the illustrations in Figures 3 and 4. 
The acquirement of good form adds considerably to 
the ease and accuracy of the writing movement, or of 
any other activity. 

Speed and quality should progress together. An- 
other question of method is related to this issue be- 
tween movement and form. Those who emphasize 
movement to the exclusion of form often require the 
child to write very rapidly from the start, while those 




Fig. 3. CORRECT POSITIONS OF BODY, AND ADMISSIBLE POSITIONS 
OF THE HAND FOR YOUNG CHILDREN 

Body position from C. P. Zaner, Zaner Method, Manual no. 1. Hand positions 
from W. A. Whitehouse, The Modern Writing Master, vol. I, no. 1. (With the 
permission of the publishers.) 




Fig. 4. INCORRECT POSITIONS OF THE HAND 

From W. A. Whitehouse, The Modem Wrifinr/ Master, vol. i, no. 1. (With the 
permission of the publisher.) 



HANDWRITING 27 

who emphasize form chiefly pay little attention to 
speed, particularly at the beginning. The practice of 
allowing the child to write excessively slowly was criti- 
cized above on the ground that it does not give the 
pupil sufficient practice. It may also be criticized on 
the ground that it does not give the pupil practice in 
connecting the elements of the movement to make a 
continuous process. When the child makes the letters 
by a slow, drawing movement, he is not obtaining a 
sensation of the whole movement in such a way that 
he learns how it feels to write a letter or a word. On 
the other hand, if the child is required at the beginning 
to make the movement as rapidly as he will later, it is 
impossible for him to form the letters correctly. As a 
consequence he is not learning to make the movements 
which he will later have to make. He is also forming 
habits of carelessness and is failing to get a clear and 
correct idea of the form of the letters. The solution of 
this question, then, is that the child should progress 
in accuracy and form together. 

The child should be able to trace his own progress. 
It follows, from this analysis of the quaUties of good 
writing, that the child should be able to trace his prog- 
ress in both quality and speed. The more definite 
his attainment can be made, the more stimulus he will 
receive toward improvement. The common method 
of grading the child's attainments by comparing him 
with others in a rough, general way is very deficient, 
because it does not give him a sufficiently definite idea 



28 PSYCHOLOGY OF COMMON BRANCHES 

either of the degree of skill which he has attained or 
the direction in which his improvement should proceed. 
The child should, then, be compared with his own past 
record rather than with that of other pupils, and this 
should be expressed in a form as definite as possible. 
The speed may be measured by occasional tests and 
the quality by analyzing it by the method which was 
suggested above. 

The correct habit should be practiced in all writing. 
We have already seen that a person's writing habit 
may be of one sort when he is writing for the sake of 
good form and of another sort when he is writing to 
express thought. The child should so develop his 
writing habit that much the same result appears in the 
ordinary work as in the writing lesson. In order that 
this may be the case, it is necessary that some atten- 
tion be paid to the writing which he produces in the 
rest of his school work. It would be well to do this 
throughout the latter part of the elementary school. 
In the first three or four grades the child's attention 
should not be distracted from the thought which he is 
expressing by the necessity of thinking much about the 
quality of the writing. He has great dijEculty at the 
best in expressing his thoughts in writing at this time, 
since the unfamiliar habit distracts his mind; but in 
the later grades it will not distract the child to exer- 
cise a little care in order that the writing shall not 
deteriorate. It is well, then, to give the handwriting 
grade upon the quality of the work which is turned 



HANDWRITING 29 

out in the other subjects as well as that which is pro- 
duced in the writing lesson. In fact, this should prob- 
ably be the main stimulus to progress in writing in 
the upper grades. 

Modifications due to age 

Motor ability changes with age. What has been 
said indicates that it is necessary to modify the method 
of teaching writing to suit the age and stage of devel- 
opment of the pupil. Some methods of teaching writ- 
ing which are in wide use take no account of the difTer- 
ence in ability of the child at different ages. For 
example, the same speed in writing is required of the 
first-grade child as of the eighth-grade child. Studies 
of the motor ability of children at different ages indi- 
cate that there is a marked increase in the rapidity of 
movement and in the steadiness and precision of move- 
ment from the age of six to that of sixteen. A study of 
the ability of children in different grades in making 
a series of upward and downward strokes as rapidly 
as possible demonstrates the same fact. A survey 
of the rapidity of writing, in all the grades from the 
second to the eighth among over thirty thousand 
children, shows that on the average the first-grade 
pupil writes less than half as fast as the eighth-grade 
pupil. 

The fundamental and accessory movement theory. 
The difference in ability between the younger and the 
older child has sometimes been ascribed to the devel- 



30 PSYCHOLOGY OF COMMON BRANCHES 

opment from fundamental to accessory movements.* 
The theory is that the younger child is able to make the 
so-called fundamental movements more readily than 
the accessory movements, and that improvement in 
ability is chiefly in gaining control over these accessory 
movements. The distinction between the fundamental 
and accessory movements is not always clear. The 
fundamental movements are sometimes described as 
those which are old in the race, such as walking; while 
the accessory movements are those which have been 
acquired in human life, such as manipulation. Some- 
times the distinction is made between the movements 
of the large muscles, or large movements, which are 
designated as " fundamental," and the opposite kind 
of movements which are called " accessory." Finally 
fundamental movements are sometimes described as 
" central," that is, concerned with the trunk or with 
the parts of the limbs next to the trunk, while accessory 
movements are those toward the extremities. An 
examination of the movements which are made by the 
young child will indicate that this distinction is not a 
very useful one. In the problem of learning we are 
not concerned with instinctive movements, and other 
movements do not develop in any consistent way from 
central to peripheral or from large to small. 
The suitability of movements for the child should be 

^ A fundamental movement is one which is old in the history of 
the race, is a large movement or is made with large muscles, and is 
central (in or near the trunk). An accessory movement is the 
opposite. 



HANDWRITING 31 

judged on the score of their rapidity, precision, and 
complexity. A much more valid distinction between 
the movements which are suited to the younger child 
and the older child rests on the facts which have 
already been referred to. The young child is not capa- 
ble of very rapid or precise movements. To this may 
be added the further fact that movements are diflBcult 
for him in proportion to their complexity. The com- 
bination of a large number of movements in one com- 
plicated coordination presents difficulties to the child 
in proportion to his deficiency in motor control. 

The difficulties should be lightened for the young 
child. These characteristics of the child make the 
acquirement of handwriting a difficult matter for him 
and one which is attended with considerable nervous 
strain. Care must be taken, therefore, to ameliorate 
for him the difficulty of the task. This may be done 
by making the requirements for accuracy and rapidity 
low and by placing the handwriting period at a time 
when the child is not fatigued. The requirement for 
speed has already been discussed. The avoidance of 
undue accuracy of form may be reached by allowing 
the child to write very large. At the beginning the 
writing should be done on the blackboard. When the 
child first uses paper, he should write with large letters 
and with a pencil which offers little difficulty in its 
manipulation. The pencil should be fairly large and 
the lead smooth. The paper should also have such a 
surface that the mark is easily made upon it. As the 



32 PSYCHOLOGY OF COMMON BRANCHES 

child grows older and gains in skill, the writing may 
be gradually decreased in size and may become gradu- 
ally more precise. 

Individual differences and 'practice periods 

Individual differences. Besides these differences due 
to age, there are wide differences between individual 
children in this as in other forms of ability. Some chil- 
dren are superior in their writing ability to the average 
of several grades above them, whereas others are equal 
only to the average of several grades below. These 
individual differences may be taken account of in sev- 
eral ways. The ideal method would be to group chil- 
dren according to their ability in each separate kind of 
work, so that those of like ability are together and that 
those who have reached a certain standard might be 
relieved of further work in that subject. This, however, 
is not possible so long as the rigid grade system main- 
tains, and the best that can be done is to recognize the 
differences among children of the same grade and to 
adjust the demand made upon the different children 
according to their various abilities. As was suggested 
above, each child should be judged on the basis of his 
past performances instead of by comparison with his 
classmates. In the speed of writing it is very desirable 
to have as many of the children as can comfortably do 
so engage in rhythmic exercises to music or to time 
marked in some other manner, but it is necessary that 
the children who do not naturally fit in with this 
rhythm should not be required to follow it. 



HANDWRITING S3 

The length of practice periods. In arranging the 
conditions so that the practice will be most effective 
in producing improvement, it is necessary to take 
account of the principles of economy in effort due to 
the arrangement of the periods of practice. It has been 
found by experimental investigation that the length 
of period or the interval between the periods of prac- 
tice affects the rapidity of learning. In the case of the 
development of a motor habit, such as handwriting, 
the same amount of time split up into rather short 
periods is more effective than if it is all expended in 
long periods. With the child in the earlier grades ten 
minutes is probably the best length of period, and in 
the upper grades not over half an hour can be spent to 
the greatest advantage. 

REFERENCES 

1. L. P. Ayers: Scale for Measuring the Quality of Handwriting of 
School Children. Bulletin no. 113, Division of Education, 
Russell Sage Foundation. 

2. L. P. Ayers: Scale for Measuring the Quality of Handivriting of 
Adults. Bulletin no. E138, Division of Education, Russell Sage 
Foundation. 

3. Frank N. Freeman: The Teaching of Handwriting. Houghton 
Mifflin Company. 1914. 

4. Frank N. Freeman: An Experimental Study of Handwriting. 
Psychological Monographs. 1914. 

5. Charles H. Judd: Genetic Psychology for Teachers. D. Appleton 
& Co. (1903), pp. 84-97 and chap. vi. ■ 

6. S. H. Rowe: Habit Formation and the Science of Teaching. 
Longmans, Green & Co. 1909. 

7. E. L. Thorndike: "Handwriting." Teachers College Record, 
Columbia University. 1910. 

8. W. A. Whitehouse: "Correct Penholding." The Modern Writ- 
ing-Masier. Boston, Mass. (1906), 1, 24-37. 



CHAPTER III 

DRAWING: PERCEPTUAL LEARNING 

In learning to write, the child develops habits of 
movement and acquires the recognition of form, but 
since the motor coordination is the more prominent 
element, writing is taken as an illustration of sensori- 
motor learning. Drawing also includes both the recog- 
nition of form and its representation, but in this case 
the element of recognition is more prominent, and 
therefore drawing is taken as an illustration of per- 
ceptual learning. Drawing is commonly regarded as 
an illustration of the development of motor habits. 
The production of the form upon the paper is thought 
of as the chief element in the process. This, however, 
is a secondary part of the whole process as will be made 
clear by the following illustration. 

A demonstration experiment in drawing 

In order that the reader may have in his experience 
a concrete illustration of the development of the recog- 
nition of form, the following simple experiment may 
be performed. Upon page 36 will be found a figure 
(Figure 5) which should not be looked at until the 
directions given below have been read and clearly un- 
derstood. The figure is to be observed for the brief 



DRAWING 35 

interval of ten seconds, after which the attempt should 
be made to reproduce it. During the time the drawing 
is being reproduced, the book should be turned over so 
that it cannot be seen. After the figure has been com- 
pleted as well as possible, the paper should be folded 
so as to conceal the drawing and another attempt made 
in the same manner. This process should be repeated 
until the experimenter is satisfied that the drawing is 
reproduced substantially in its correct form. It is not 
necessary that it shall be minutely accurate, but only 
that the chief elements shall be present in about their 
true relations. 

The act of drawing has produced completer recog- 
iiition. After the drawing has been made, the reader 
should analyze his experience and test the correctness 
of the following account. The first question for exam- 
ination concerns the difference between the perception 
of the figure after the figure has been drawn in the 
final trial in comparison with the type of recognition 
which existed before it had been mastered. It is clear 
that, as a result of the study and the attempt to repro- 
duce the figure, something has taken place which 
materially modifies the recognition of it. This has not 
been in the nature of mental development in general, 
but has rather consisted in the development of the 
ability to recognize this particular figure. Before the 
study, the figure was seen in a vague, indefinite man- 
ner. It was noticed that there were a number of lines, 
but the shape of the lines or their exact relationship 



36 PSYCHOLOGY OF COMMON BRANCHES 

to each other was seen only very vaguely. In this first 
preliminary recognition some persons emphasize more 
the general outline of the figure and others recognize 
one or two details clearly, but lose sight of the rest. 
Whichever type one belongs to, after the study of the 
figure, one is able to grasp the general outline and at 
the same time the details of which it is composed. 




Fig. 5 

Completer recognition is gained through active 
exploration. The next question to be considered is the 
means by which the development has been attained 
which results in this different manner of recognition. 
In the great majority of cases, when the question is 
raised, it will be found that one has begun the study 
of the figure at a particular point, usually the left end 
of the figure. It is instructive to ask ourselves why 
most people begin at the left end rather than at the 
right end. The explanation is undoubtedly to be found 
in the fact that we have learned to recognize words on 



DRAWING 37 

a printed page in this order and that we have learned 
to write from left to right. This means, then, that we 
bring to the study of this figure certain habits of explo- 
ration which determine the kind of procedure we shall 
take. 

General ideas are employed. There are also other 
features of the process of studying the figure which 
indicate the existence of a definite series of mental 
habits based upon our past experience. For example, 
the number of lines was very likely determined by 
counting. In this we use the general idea of number 
or the habit of thinking of things by number as instru- 
ments in developing the recognition of the figure. Very 
likely also the kind of lines was noted and it was seen 
that there were some straight lines and some curved 
lines. The alternation of the straight and curved lines 
was likely also to have been observed, and the fact 
that the lines formed angles with one another and 
that these angles were perhaps of about so many 
degrees. Very often the figure is grasped by com- 
paring it with familiar objects, such as a letter of 
the alphabet, or stenographic signs. 

The nature oj 'perception as illustrated in drawing 
Development of perception consists in organizing 
impressions, not in gaining new ones.^ This description 
of the way in which we set about such a task will show 

* Formal definitions of perception and sensation are given on 
p. 51. 



38 PSYCHOLOGY OF COMMON BRANCHES 

that we bring to it a vast number of ideas and habits 
of procedure out of our past experience and that our 
mode of gaining a mastery of the figure is not passively 
to allow it to make an impression on the mind, but 
rather actively to go about its study, using these ideas 
and habits of procedure. We may sum up this experi- 
ence by saying that the recognition of such an object 
is not chiefly a matter of gaining impressions, but 
rather a matter of actively analyzing the characteris- 
tics of the object. Put in another way, this principle 
means that the development of the ability to recognize 
such an object is not primarily the development of 
keenness of the senses, but rather the development 
of a mode of arranging or organizing the sensations 
which we receive from the object and giving to them a 
meaning. 

Such organization includes analysis and synthesis. 
The analysis of such a figure into its parts makes pos- 
sible the grasp of the figure as a whole. In the final 
recognition we were not merely able to see each part 
clearly, but we were able to grasp a larger number of 
the parts because each one had previously been studied 
for itself. The whole process consists of the clearer 
recognition of the parts and better organization of the 
parts in relation to one another. Put in technical 
terras, such recognition is based on both analysis and 
synthesis. 

Example of the manner of directing the child in the 
development of his perception. The fact that in order 



DRAWING 39 

to gain a clear perception of an object it is necessary 
to go about the study of it in an active manner finds 
illustration in all the work of the school in which a 
study is made of concrete objects. It gives the clue to 
the manner in which the teacher can guide the child's 
efforts to gain an accurate and comprehensive notion 
of such an object as a plant or an animal. The child 
should not be allowed merely to get a vague impression 
by passively looking at the object, but he should be 
led, through questions and discussion, to examine the 
various parts in detail and to discover their likenesses 
to the parts of other similar objects or their differences 
from them. Thus, in studying a cow the child should 
be induced to examine its teeth, to compare them with 
the teeth of the sheep, the horse, the dog, cat, etc. 
These facts are then to be related to the different kinds 
of food which are eaten by the different classes of ani- 
mals. In similar manner the child examines hoofs, 
horns, etc. As he gains a clearer idea of these details 
he is also at the same time putting them together so 
that they combine to give him a complete notion of 
the animal as a whole. 

Past experience is involved in all perception. These 
characteristics are true of our perception in general. 
One of the most prominent characteristics of percep- 
tion is that we depend for our recognition of things in 
large measure upon the result of our past experience. 
The bearing of our past experience upon our present 
recognition and responses is easily recognized in cases 



40 PSYCHOLOGY OF COMMON BRANCHES 

in which the differences due to differences in past 
experience are more obvious. In such cases the activity 
of past experience in governing interpretation is called 
" apperception," Many objects have a widely differ- 
ent meaning to different persons because of their past 
training or education. The artist sees in a rural scene 
the beauty of the landscape; the farmer, on the other 
hand, may see the possibility of raising crops; the 
huntsman may think of it as containing game; and 
so on. 

All perception is apperception. The bearing of past 
experience in such cases is obvious, but it is equally 
present in every recognition. The setting-off of a few 
of our experiences as being characterized by appercep- 
tion^ as distinguished from others which we call "per- 
ception " obscures this fact. Apperception is present 
in every case of perception, and is therefore not any 
unusual or peculiar characteristic of mental life, but 
is rather present throughout its whole range. 

Object teaching is not merely showing the child 
objects. The practical application of this principle is 
that different persons will give a different interpreta- 
tion to their experiences because of the different back- 
ground in which they are set. We recognize this in the 
case of the more conscious interpretations we make, 

^ Apperception is a broad term which designates the part played 
by the mind itself in determining the character of our experience. 
What our experience is depends on our inherited cast of mind and on 
our previous experience as well as upon the stimuli which affect us. 
This activity of the mind in coloring experience is apperception. 



DRAWING 41 

but it is also of great importance even in the perception 
of physical objects. The mistake is sometimes made of 
supposing that when we set up an object before a child 
his recognition of it is the same as ours. Object teach- 
ing does not merely consist in presenting things to the 
child, but rather consists in giving him such modes of 
interpretation that he can see in the object the thing 
which the educated person sees. Likeness in the stim- 
ulus does not guarantee likeness in the response. There 
must be also a similarity in the form of development 
of the two persons who are making the response. 

Illustration of the need of past experiences as a 
background for the complete recognition of objects. 
The task of the school with reference to the child's 
recognition of the objects of the world about him is 
systematically to furnish him with experiences or use 
the experiences which he has so that he will have an 
adequate background for their interpretation. One of 
the common objects of the modern person's environ- 
ment is the trolley car. To the majority of the adults 
of the present, who did not learn about electricity in 
their school days, the trolley car is a mystery. They 
know there is something called electricity, which trav- 
els along the trolley wire, and that when the trolley 
is in contact with the wire and the motorman does 
something with the handles before him the car starts. 
In order to see more than this in a trolley car one has 
to become familiar with the dynamo and electric 
motor, to learn how a wire passing through a magnetic 



42 PSYCHOLOGY OF COMMON BRANCHES 

field generates an electric current, and that when a 
current passes through a wire which is in a magnetic 
field motion is generated. One thus comes to see that 
the electric current is a means by which the motion 
which is generated at the power-house through steam 
or water power is reproduced at the wheel of the trolley 
car. Thus we see that the complete recognition of a 
trolley car depends on having a great many prelim- 
inary experiences. 

Drawing (with the other representative arts) selects 
particular features for representation. The influence 
of past experience upon the type of recognition has a 
particular illustration in drawing. Drawing is not a 
photographic representation of all that is seen. There 
is always, either consciously or unconsciously, a 
selection of features of the total appearance to be 
represented. The history of the development of the 
arts of drawing and painting indicates that those 
aspects of objects which are selected to be represented 
vary with the stage of progress which an art has 
reached. The ultra-modern schools, as the Cubists 
and Futurists, are attempting to develop new modes 
of representation which will depict aspects hitherto 
not represented, such as motion. 

Representation by drawing depends on the mastery 
of a drawing language. Learning to draw, in fact, may 
be thought of as an acquirement of a language or a 
mode of expression. This language has gone through 
stages of development just as has spoken language. 



DRAWING 43 

The early Egyptians were able to reproduce certain 
characteristics of the form of objects, but lacked 
entirely the ability to represent perspective, or the 
differences in the distances of objects, by means of the 
hues of their drawing. One object was represented as 
being farther away than another merely by being 
partly hidden by it. We may speak of the Egyptian 
mode of representation, then, as one sort of dialect of 
the drawing language. We may also compare the art 
which has been developed in Oriental countries with 
that of our own, and we find here also two different 
dialects. Chinese and Japanese painting, for example, 
consists chiefly in the use of lines instead of the masses 
which are used in Western painting, and until recently 
Occidentals failed to appreciate the significance of 
these drawings. 

One sees, in a measure, what one can represent. 
These differences in mode of representation are not 
merely differences in expression, but also represent 
different modes of seeing the object. A person who has 
had one type of training sees a particular aspect of the 
thing and represents that aspect because he has ac- 
quired the mode of representation which is suited to it. 
He has developed a tool of expression, and as a con- 
sequence he can see the things which are capable of 
representation by this tool. 

In his early experience the child learns to recognize 
the real form from the appearance it presents. An 
example of the way in which drawing serves as a mo- 



44 PSYCHOLOGY OF COMMON BRANCHES 

tive to seeing things in a different manner or in a more 
adequate manner may be taken from the development 
of the child. When the child begins to draw, he is not 
able to represent perspective by means of the lines and 
their relationship to one another. The reason for this 
is that he draws the objects which he sees as he knows 
them to be rather than as they appear from a particu- 
lar point of view. He has learned to see the object as 
it really is and not to recognize the particular appear- 
ance which it presents as he looks at it. The child's 
form of recognition is one which he has bought at the 
expense of a good deal of time and experience. When 
the child first observes objects, he is undoubtedly 
impressed by their appearance, and he does not at 
first realize that an object which presents one shape 
from one point of observation and another from an- 
other point is really an object which has its own con- 
stant shape independently of the position from which 
it is viewed. He learns this lesson thoroughly. For 
example, he knows that the top of a table is rectangular 
in spite of the fact that it appears from most positions 
to have acute and obtuse angles. When now he draws 
a table, he represents it in this rectangular shape. 

Drawing is the representation of the appearance. 
The difficulty in learning to represent perspective, — 
that is, to draw the object as it appears from a particu- 
lar point of view, — is that we are incapable at first 
of clearly recognizing how the object does appear. One 
must, then, learn to give attention to the appearance 



DRAWING 45 

in order that he may reproduce this on paper, and thus 
give the impression which the object makes upon him. 

The recognition of the appearance comes from try- 
ing to draw it. The child acquires this abihty to pay 
attention to the aspect of an object which is presented 
from a particular point of view only through the 
acquirement of technique of expression. Merely to 
lecture to the child upon perspective or to discuss the 
principle of vanishing points, horizon, and so on, as 
was formerly done, does not give him the form of 
recognition which he needs. The best method of doing 
this is to lead the child to experiment in putting lines 
in different relationships to one another so that they 
shall correctly represent the object which is being por- 
trayed. For this purpose the three lines which repre- 
sent the three dimensions of an object may serve as 
the basis of experimentation. After the child has 
learned to place these lines in such a way that they 
represent the appearance of a chair, say, or of a table, 
he has acquired an added ability in seeing as well as a 
new mode of expression.* 

Illustration of the bearing of activity on perception. 
As the recognition of form is made accurate and com- 
plete by the active response of drawing, so also do the 
active responses which we make influence very greatly 
all our perceptions. We see and hear and touch in 

' This is the method pursued in the University Elementary School 
of the University of Chicago under the direction of Professor Walter 
Sargent. 



46 PSYCHOLOGY OF COMMON BRANCHES 

order that we may effectively move and handle and 
use. Sensations exist to guide actions. Therefore, the 
natural and most effective stimulus to perception is a 
demand for action toward the object in question. A 
boy who has a chance to run an engine or an automo- 
bile will soon find out enough about it for his practical 
purposes, and the practical impetus which he thus 
gains may carry him a good deal farther in his investi- 
gations. Not only so, but the experience he has gained 
in actually handling the machine gives him a far better 
understanding and basis for further knowledge than 
merely looking at it would have given. In a similar 
way the girl is led to a far more intimate and exact 
knowledge of food materials and cooking processes 
by a little practical experience, accompanied by the 
appropriate theoretical study, than by theoretical 
study alone. 

Development of drawing with age 

Children develop chiefly in the comprehension of 
complex forms. The ability of the child to represent 
objects varies to some extent with the stage of his 
development. The stage of development is based to a 
small degree upon the skill with which the pencil can 
be handled, but also to a much greater degree upon 
the extent to which the child can analyze an object and 
can comprehend the different parts of it in relation to 
one another. A test which has been made of school 
children of different ages indicates that the younger 



DRAWING 47 

and older children do not differ greatly in their ability 
to reproduce simple forms. ^ The individual differences 
among children in this respect are more prominent 
than are the differences between children of different 
ages. The suitability of a figure to the age or stage of 
development of the child would seem to be based more 
on its complexity than upon the accuracy with which 
a particular part must be observed or reproduced. 

The young child's drawing is symbolic. Studies of 
the drawings of children indicate that there is a marked 
difference in the degree to which a child delineates the 
individual characteristics of an object, or the details 
of which it is composed. The child neglects the char- 
acteristics which distinguish an object from others of 
the same kind and represents only such features as 
enable another person to know the general class to 
which the object belongs. We express this fact by 
saying that the drawing of a child is symbolic. At 
about nine years of age the child seems to recognize 
more clearly the need of more accurate and detailed 
representation. An illustration of this transition ap- 
pears in the fact that before this age the majority 
of children draw a face from the front view, whereas 
after this age the majority draw it from the side view. 
The side view is a much easier one to represent, and 
when the child endeavors to represent accurately, he 
chooses the easier mode. 

* From an unpublished master's dissertation by S. P. Chinnappa, 
on file in the library of the University of Chicago. 



48 PSYCHOLOGY OF COMMON BRANCHES 

Pictorial representation develops rapidly from the 
transition stage to adolescence. The two elements of 
pictorial representation which indicate its progress are 
the increase in the fullness and accuracy with which 
the particular characteristics of the individual objects 
are presented, as distinguished from the presentation 
of the characteristics merely which belong to the gen- 
eral class of which the object is a member, and the 
representation of perspective. The portrayal of per- 
spective may be regarded as an artijBcial performance 
in the sense that it requires a type of attention to the 
appearance of objects which is not produced by the 
ordinary demands of life, but is due to the special 
demand of representing relations in three dimensions 
on a two-dimension surface. That this is counter to 
the usual type of perception is shown by the fact that 
it took the race so long to develop it. Early Egyptian 
art is almost completely lacking in perspective, the 
Greeks attacked the problem but did not solve it, and 
it was left for the painters of the Italian Renaissance 
finally to develop the true representation of depth by 
drawing. It is not surprising, therefore, that the child 
does not represent perspective in his early drawing, 
and its development is to be looked upon as depend- 
ent upon the acquirement of the intellectual capacity 
necessary to enable him to understand and adopt the 
methods which have been handed down rather than 
as a spontaneous growth. 

Mechanical drawing and diagramming represent 



DRAWING 49 

structure and relations of parts. Mechanical drawing 
and diagramming more closely resemble in purpose 
the drawing of the young child than they do pictorial 
drawing. The distinction between diagramming and 
pictorial drawing is brought out sharply in an investi- 
gation, as yet unpublished, by Dr. Frederick C. Ayer. 
The subject of Ayer's study was the relation of draw- 
ing to the work in science. He first found that there 
was little relation between the student's ability in 
pictorial drawing and his rank in science work. He 
then studied the correlation between the ability to 
draw a diagram — for example, of the minuter struc- 
ture of a feather, as seen under a low-power microscope 
— and ability in science. Diagramming calls for the 
analysis of the object into its parts and the comprehen- 
sion of the relation of these parts. The drawing does 
not need to look like the object so long as it gives the 
observer the idea of the relation. Similarly, mechanical 
drawing does not give a realistic picture of the object. 
A plan drawing or an elevation represent only one 
face of an object, and often internal structure which 
cannot be seen at all; and in representing the parts 
which can be seen only shows enough to indicate the 
structure. Even a mechanical drawing in perspective 
is constructed according to rule, shows the object from 
a set point of view, and indicates the structure only. 
It can be made by any one who knows the rules and is 
careful in making his measurements and drawing his 
lines accurately. A comprehension of the structure of 



50 PSYCHOLOGY OF COMMON BRANCHES 

the object and skill and accuracy in measurement and 
drawing are required, but not ability in recognizing 
relations in space as they appear to the eye, or the 
ability to reproduce these appearances. 

Diagramming begins early, mechanical drawing at 
about adolescence. As has already been suggested, 
the child's early drawing is a crude sort of diagram- 
ming. His development in this type of drawing is 
dependent mainly upon the development of his ability 
to analyze objects and to understand their relations. 
Mechanical drawing, because it usually requires a 
conception of internal structure, and always accuracy 
in measurement and drawing, does not develop in any 
large degree until about adolescence. 

Individuals differ in their rate of development and 
in the stage which is finally attained. While the devel- 
opment in accuracy, as represented by correctness of 
detail or by the degree to which perspective is shown, 
develops rapidly up to adolescence, there are individual 
differences in this respect, as in the others which have 
been mentioned. Very many children do not at ado- 
lescence equal the stage of development which others 
have attained several years before. In suiting the 
form of training to the child, then, the development 
which is characteristic of the average child must be 
taken into account, and also the different stages of 
development which different children represent at the 
same age. 



DRAWING 61 

General account of the nature of perception 

In perception impressions or sensations are given 
an interpretation. The illustration of drawing has 
shown that the recognition of objects which are strange 
is not by any means a simple affair. When a child 
recognizes the form of a figure, as we have seen, he 
brings to bear upon the sensation which he receives 
through his eye the ideas and the habits of attention 
and of recognition which have been formed by his past 
experience. This application of past experience to our 
present impressions makes possible the interpretation 
of the sensations through which they acquire a mean- 
ing. When we receive a sense impression and add to it 
the results of other experiences in order to give it an 
interpretation, we call the mental process " percep- 
tion." ^ In perception we usually bring to bear upon 
the impression the results of past impressions which 
have been received both through the same sense, and 
also through different senses. This whole process of 
recognition through the association of other experi- 
ences which we have had in the past may be illustrated 
by another example. 

* A sensation is a simple experience which is produced by the 
stimulation of one of the sense organs; as, for example, the impres- 
sion of a color, or a sound, or of a taste, or of a touch. Such a simple 
experience does not of itself have any meaning. A perception is a 
sensation which has acquired a meaning through its combination 
with other sensations. In perception there is the recognition of 
objects, while in sensation only a single quality is experienced. 
Sensation is an incomplete stage in the development of perception. 



52 PSYCHOLOGY OF COMMON BRANCHES 

Illustration of the complexity of perception. We 
may take as an example the recognition of a cup of 
milk by the child. The impression which the child 
receives as he looks at the cup is one of sight, or of 
vision. He sees the color of the cup; he recognizes its 
outline, or its form. In addition to this, however, he 
thinks of the cup as having a certain degree of hard- 
ness; that is, he recognizes that if he should touch the 
cup it would offer resistance to his finger, and he does, 
not attempt to compress it as he would a rubber ball. 
In this recognition he is applying the results of the 
previous experience gained through handling the ob- 
ject. Further, he recognizes that the cup has a cer- 
tain weight. If he thinks of it as being full of milk, 
whereas in fact it is nearly empty, and if he then 
attempts to lift the cup, he will exert too much force. 
This may result in such application of force as to cause 
the milk to be spilled. This gives an evidence that 
there was in the recognition also a notion of the amount 
of force necessary to lift the object. The child also has 
some recognition of the sound which would be made if 
he were to knock the cup against some other object, 
and this expectation is illustrated when he strikes a 
spoon against the cup. If it gave forth a different sound 
from that which it usually gives he would exhibit 
surprise. 

There is also a variety of present impressions. In 
addition to this obvious combination of the results of 
past experiences of different senses, there is also a 



DRAWING 53 

combination of different impressions received through 
the two eyes. It is a well-known fact of psychology 
that the recognition of the distance of objects depends 
on the fact that we get a slightly different view of an 
object through one eye from that which we get through 
the other. These two views are combined in our per- 
ception, and as a result of this fusion we recognize the 
distance. Furthermore, the fact that our eyes have to 
turn inward more to look at a near object than to look 
at a far one gives us an experience of muscular strain 
which we may use in distinguishing distances. When 
the child turns his head to look at the cup, he also gets 
sensations from the muscles and joints of the neck, 
which gives him a recognition of the direction of the 
object from his body. 

Such a perception is a result of growth. This analy- 
sis of the various elements which go to make up such a 
simple perception as this is of no particular value 
merely as showing that the experience is a complicated 
one. Its value is rather in indicating that this percep- 
tion must have had a growth or development; that it 
is not something which the child has merely as a result 
of the structure of his sense organs. Theories of per- 
ception have sometimes been held which assume that 
the object impressed itself upon the mind, or upon the 
sense organs. On the contrary, the recognition of the 
object is built up as a result of a variety of past experi- 
ences and through a combination of a number of differ- 
ent present elementary experiences. 



54 PSYCHOLOGY OF COMMON BRANCHES 

Development is Hlustrated in overcoming illusions. 
We must not expect, then, that the recognition of the 
child is precisely the same as that of the older person. 
As it is a result of growth, so the stage of growth which 
has been reached in the child's mind is different from 
that which has been reached by the adult. Experi- 
ments have shown that recognition of objects by the 
adult is not perfect. The person who has had experi- 
ence in drawing, for example, has a more complete 




Fig. 6. MULLER-LYER ILLUSION 

recognition of form than has the ordinary individual. 
Studies in optical illusions,^ an example of which is 
shown in the accompanying Figure 6, indicate that 
while the ordinary person makes a large error in com- 
paring the length of the lines in the recognition of such 
a figure, he may overcome the error by sufficient prac- 
tice. After about one thousand trials one can judge 
correctly the relative length of the two lines. 

^ An illusion is a false or distorted perception. It is not com- 
monly abnormal, but is a form of misinterpretation, common to 
nearly all persons, which can be explained by ordinary psychological 
principles. 



DRAWING 55 

Sensations at first become combined into percep- 
tions in the recognition of an object which has prac- 
tical meaning. One might conclude, from the analysis 
of perception which has been made, that the various 
sensations are combined in perception in some mechan- 
ical way or because the child has some inner tendency 
or other to build together sensations into perceptions. 
This would be an altogether false view of the matter. 
The sensations are built together as they contribute 
to the child's recognition of an object, and in the 
majority of cases, as has been already said, the child 
learns to recognize objects which have some practical 
value or meaning to him. The cup of milk may be 
taken again as an illustration. It is clear in this case 
that the chief motive of the child in paying attention 
to the cup and in learning to recognize its form, direc- 
tion, distance, weight, etc., is the satisfaction of his 
appetite for the milk. Those sensations which add 
something to the recognition, so as to enable the child 
more clearly to distinguish the cup and more quickly 
and surely to grasp it and carry it to his mouth, are 
built into the perception. Others are largely neglected. 
While it is true that the child does exhibit some interest 
in sensations, in discriminating between them and in 
giving them names, he gives attention to them and 
discriminates between them chiefly because they stand 
for an object which has some practical meaning for 
him. 
Illustration: Double images are recognized as a 



56 PSYCHOLOGY OF COMMON BRANCHES 

difference in distance. The fact that we pay attention 
to those aspects of objects which have a meaning or 
significance for us, and to other aspects only to this 
end, is shown by the fact that many differences be- 
tween our sensations are not recognized except in the 
form of a meaning which is represented by these differ- 
ences. For example, if we hold two fingers before our 
eyes, one about twelve inches farther away than the 
other, and look at the nearer finger, we can make out 
a double image of the one farther away. This is due 
to the fact that the image of the far finger is not 
focused upon the corresponding parts of the retinae 
of the two eyes. This, however, is not usually noticed 
by us unless our attention is called to it; and as a 
matter of fact many people find diflBculty in distin- 
guishing two images even when the fact of their exist- 
ence is pointed out. We do not pay attention to the 
double images for themselves; the doubleness is only 
represented by a meaning — the meaning of nearer or 
farther away. 

Another illustration : A difference in the loudness of 
a sound as heard in the two ears means direction. A 
still more striking example may be taken from the 
experiences which we have from the two ears. If a 
sound is given midway between the two ears, we 
receive substantially the same sensation in both, and 
it is very difficult to give the exact location to the 
sound. If, however, the source of the sound is at one 
side, the loudness and the quality of the sensation in 



DRAWING 67 

the two ears is different, and we interpret this differ- 
ence as meaning that the sound comes from a given 
direction. We cannot tell from the examination of our 
sensations themselves that we get any different sensa- 
tions in the two ears. The fact that the perception of 
direction is based on the difference in the sensation 
from the two ears may be very strikingly confirmed 
by giving two sounds simultaneously to the two ears 
at different distances. This may be done by means of 
two telephone receivers which are in the same circuit. 
Under these circumstances we recognize a single sound, 
not in the real direction of either of the two soimds, 
but rather in an intermediate direction, which corre- 
sponds to the position of a sound which would give the 
same relative loudness to the two ears as is given by 
the two separate sounds. 

One may distinguish finely in some fields and 
coarsely in others. A good example of the place which 
meaning has in directing our attention to a discrimina- 
tion between sensations is given by Kirkpatrick. He 
shows that the same person may discriminate finely in 
certain fields, and much less finely in others. The prim- 
itive man, for example, is able to discriminate very 
finely between signs which represent to him the pas- 
sage of an animal or of a human being through the 
woods. The same signs pass entirely unnoticed by the 
civilized person. On the other hand, the savage is 
unable to discriminate between the small and intricate 
marks on a page which to the civilized person who has 



58 PSYCHOLOGY OF COMMON BRANCHES 

learned to read are entirely clear and easily distin- 
guished. The difference is, of course, that the printing 
has significance to the civilized person, and he has 
therefore learned to discriminate in that field. This 
whole matter will have a practical apphcation in the 
discussion of the question of sense training. 

Perception is influenced more by the development 
of meanings than by increase of ability in discrimina- 
tion. The foregoing discussion will give a basis for 
the distinction between the type of perception of the 
child and of the older person. The development of 
perception which takes place with the advancing age 
of the child does not consist primarily in the ability 
to make fine discriminations. The young child can be 
trained to discriminate more accurately than does the 
average adult. The ability which the child develops 
with his education and with advancing age is the 
abihty to pick out of a whole situation certain aspects 
of it which will have significance. If a child and an 
adult walk down the street together and are ques- 
tioned afterwards about what they have seen, it will 
be found that the child has seen more miscellaneous 
things than the adult. His mind is open to impressions, 
but it is not directed to gathering impressions of any 
particular sort. If his attention happens to be at- 
tracted in a particular direction he will observe what 
is going on very minutely. The adult, on the other 
hand, is likely to observe some particular sort of facts. 
If he is a botanist and is walking through the woods, 



DRAWING 59 

he will observe the forms of plants, of flowers, etc., 
with great accuracy and minuteness; not because he 
has greater power of discrimination among sensations, 
but because he knows what to look for, and knows the 
significance of what he sees. 

The child must develop habits of observation. We 
may say, then, that the development of the child con- 
sists in the formation of habits of recognition, or of 
habits of observation in particular directions. This 
may, it is true, close his mind to the observation of 
other sorts of facts, so that the young child may ob- 
serve a great many things which will be hidden from 
the older person. The young child may be less easily 
misled by the method of the sleight-of-hand performer, 
which consists in attracting the attention of the audi- 
ence toward one point while the trick is being done 
somewhere else. One cannot rely on the child to keep 
his attention on the spot where the performer intends 
it to be directed, because he has not yet formed suffi- 
ciently stable habits of observation. 

The child is suggestible in reporting what he has 
observed. The child is more easily deceived or more 
suggestible than the adult in other ways. Having had 
less experience as to what is likely to happen, he is 
more ready to believe that anything which appears to 
be true has actually happened. Furthermore, in recall- 
ing what he has observed, he is more apt to confuse 
what he has actually observed with what he has not, 
but in spite of this unreliability he has a most implicit 



60 PSYCHOLOGY OF COMMON BRANCHES 

faith in his ability to report faithfully what he thinks 
he has observed. Finally, he is more subject to per- 
sonal influence than the adult in concluding that he 
has or has not observed any facts which may be in 
question. This makes it necessary to use a great deal 
of caution in questioning the child. It is, of course, a 
commonplace that the court does not give full recogni- 
tion to testimony given by children, because of the 
ease with which they are led to think they have experi- 
enced that which they have not. The same caution 
should be observed in questioning the child in school. 
There is danger that the child will merely follow the 
cue given by the teacher in the question, instead of 
giving expression to his own knowledge or opinion. 
Unless one is trying deliberately to develop a senti- 
ment by means of suggestion, leading questions — or 
questions that imply their own answer — should be 
avoided. 

The distinction between subjective and objective 
observers. We sometimes hear it said that some per- 
sons are good observers in general, while others are 
bad observers. We mean by this that some persons 
are able to report faithfully what they have actually 
seen, whereas others are likely to read into what they 
have seen the results of their imagination. Some 
experiments have been made in order to determine 
whether this difference actually exists, and as a result 
the distinction has been made between subjective and 
objective observers. Objective observers are those 



DRAWING 61 

who see, perhaps, but a small number of objects, but 
see them very clearly; while subjective observers may 
take in a much larger range and give it an interpreta- 
tion, but the meaning which is read into the facts is 
apt to be erroneous and may cause the observer to 
think he has seen what he actually has not. 

Most persons belong to a mixed tjrpe. Something 
corresponding to such differences undoubtedly exist, 
although most persons do not belong to either extreme 
type. When persons are tested with reference to their 
observation in a number of different fields, it appears 
that a person may be an objective observer in some 
fields and a subjective observer in others. We may 
say, then, that most persons belong to an intermediate 
type. There are, undoubtedly, however, a few who 
are extremely unreliable and who read into what they 
see their own interpretations; while there are others 
who are very reliable and who distinguish clearly be- 
tween what they see and the meaning which they give 
to it. 

The value of sense training 

Some educators advocate much sense training. As 
distinguished from training in observation or in per- 
ception in the true sense of the term, there are a num- 
ber of educators who hold that it is desirable to train 
the child in the ability to discriminate finely between 
different sensations. This does not involve the recog- 
nition of the meaning or the interpretation of the sen- 



62 PSYCHOLOGY OF COMMON BRANCHES 

sation, but merely sensory discrimination. Illustra- 
tions of the demand for this type of training may be 
found in Halleck's Education of the Central Nervous 
System. In chapters 7 and 8 of this book the author 
advocates the training, not only of the senses of sight 
and hearing, but also of touch, taste, and smell. He 
gives a long and elaborate series of tests which may 
be made in order to develop the child's ability to dis- 
criminate and to recognize a great variety of smells 
and tastes, and of objects which give different sorts of 
touch experience. Great prominence has been given 
to the demand for such sense training also by the 
Montessori method. In this method, as applied to 
kindergarten children, many exercises are given to 
enable the child to discriminate between fine shades of 
color, between different textures of cloth, or of other 
objects, and between sounds. The belief underlying 
the advocacy of this method is that when the child's 
senses are trained, he will be enabled to observe better 
and to use the results of his observations in his thinking. 
Experience with a wide range of concrete objects is 
of great value as compared with sense training. In 
considering the value of such suggestions we must 
keep clearly in mind distinctions between sensory 
discrimination and the familiarity with objects so that 
they can be recognized and their meaning understood. 
The child may have his senses very keenly developed 
and yet know nothing of the common objects of the 
world about him. It is conceivable that the child 



DRAWING 63 

might be put into a room with a few pieces of appara- 
tus and have his senses very keenly developed, and yet 
not know such objects as a tree, a bird, a cow, a calf, 
a house, a trolley car, etc. There is sometimes failure 
to distinguish between sense training, strictly speaking, 
and this acquaintance with a large number of objects. 
This knowledge of objects was studied by G. Stanley 
Hall and reported in an article entitled " The Con- 
tents of the Children's Minds on entering School." ^ It 
was found that children were remarkably ignorant of 
many of the objects which were talked about or read 
about in the earlier grades. This lack is undoubtedly 
a great handicap to the child, and anything that is 
said in the following paragraphs in disparagement of 
sense training must not be taken to mean a belittle- 
ment of the value of a wide acquaintance with con- 
crete objects on the part of the child. 

Keen senses do not necessarily go with high intelli- 
gence. Some light may be thrown upon the value of 
mere keenness of the senses by facts which are either 
common matters of observation, or have been estab- 
lished through scientific experiments. It is well known 
that certain of the lower animals have some of their 
senses more keenly developed than the human being. 
The dog has a much keener sense of smell than has 
man. Some of the birds have a keener sense of vision, 
and some insects can hear sounds which to us are 
absolutely non-existent. The keenness of senses in 
* Reprinted in Some Aspects of Child Life and Education. 



64 PSYCHOLOGY OF COMMON BRANCHES 

these animals does not produce in them a correspond- 
ing degree of intellectual development. Furthermore, 
if we compare the sensory keenness of backward chil- 
dren, or even of feeble-minded children, with that of 
normal children, we find that there is no great differ- 
ence. In order to find striking differences between chil- 
dren of different degrees of intelligence, we must go 
to such higher mental processes as reasoning, the rec- 
ognition of logical relationships, and memory. 

Discrimination should be keen enough to meet the 
demands of perception. The discussion of perception 
and its development has shown that, in the ordinary 
course of life, we develop sensory discrimination as it is 
found to be useful to us in meeting the demands of our 
practical life; that is, we distinguish between sensa- 
tions with suflScient accuracy to enable us to get an 
accurate perception. It would be possible for us to 
develop our senses very much more highly than we 
ordinarily do. The blind person has developed a sense 
of touch in his fingers very much more than the person 
who has sight. He also has developed the sense of 
hearing more highly than has the average person. It 
is undoubtedly true that all of us could develop our 
senses more keenly than we have, but it is questionable 
whether we should find that such development repaid 
us for the effort which was expended. 

Sensory defects should be discovered and, if possi- 
ble, corrected. Whenever the child is deficient in 
sensory capacity, there is, of course, danger that his 



DRAWING 65 

mental development will suffer because of the lack of 
the proper materials with which to think. We assume, 
in the ordinary routine of school life, that the child 
can hear the directions which are given him in the 
schoolroom, and that he can see figures and words 
which are written on the board. If the child is suffi- 
ciently deficient so that he cannot hear or see these 
things, he will unquestionably suffer. It is necessary 
to find out whether a child has a degree of sensory 
keenness which will enable him to profit in these 
ordinary ways by the things which go on about him. 
It is also necessary to correct defects wherever they 
can be corrected. 

The normal child does not need systematic sense 
training as does the feeble-minded child. We must 
clearly recognize that certain senses are very much 
more important than others. Sight and hearing are of 
importance out of all comparison to taste and smell, 
and touch is intermediate between these in value. We 
must also recognize that, although sense training is of 
considerable value to the feeble-minded child, the 
normal child gets o^'^ of his ordinary experience train- 
ing which must be given to the abnormal child by 
special exercises. The normal child learns to distin- 
guish colors and shapes through the exercise of his 
natural curiosity, which prompts him to play with 
things and learn their names as he hears them spoken 
by older persons. A little special attention by the 
parent will serve to hasten this development and make 



66 PSYCHOLOGY OF COMMON BRANCHES 

the child's knowledge more exact and comprehensive. 
The feeble-minded child, on the other hand, does not 
learn the common facts of his environment spontane- 
ously, but needs special, systematic drill. It is a great 
mistake to assume, as does the Montessori method, 
that this training, which is necessary for the defective 
child, is suited to be the main part of the education of 
the normal child. 

REFERENCES 

1. E. Barnes: "Study of Children's Drawings," Ped.Sem. (1892), 
vol. 2, pp. 455-63. 

2. A. B. Clark: Children's Attitude toward Perspective Problems. 
Barnes's Studies in Education (1896-97), pp. 283-94. 

3. G. Stanley Hall: Some Aspects of Child Life and Education. 

4. R. P. Halleck: Education of the Central Nervous System. Mao 
millan (1896). chaps, vii and viii. 

5. C. H. Judd: Genetic Psychology for Teachers. D. Appleton & Co. 
(1903), chaps, i and ii. 

6. C. H. Judd and D. J. Cowling: "Perceptual Learning." Psy- 
chological Review, Monograph Supplements, vol. 8, Yale Studies 
(N.8.), vol. 1, no. 2, pp. 349-69. 

7. H. T. Lukens: "A Study of Children's Drawings in the Early 
Years," Ped. Sem. (1896-97), vol. 4, pp. 79-110. 

8. W. Sargent: Fine and Industrial Arts in the Elementary School. 
Ginn & Co. (1912), chap. i. 



CHAPTER IV 

READING: PERCEPTUAL LEARNING 

The relation of reading, writing, and spoken language 

Reading and writing are very closely related to one 
another from the fact that both are related to spoken 
language. Writing is the expression by graphic signs 
of ideas which were previously expressed in spoken 
words. Reading is the ability to recognize words which 
have been so written or printed. In both cases, then, 
we are concerned not merely with the recognition or 
production of certain forms, certain marks on paper, 
but we are concerned with the recognition or the ex- 
pression of ideas as they are represented by printed or 
written forms. The written or the printed forms on the 
paper stand for spoken words, or may be said to be the 
symbols of the spoken word, 

Reading and writing should have meaning to the 
child. The teaching of reading and of writing ought, 
therefore, to be very closely related to the meanings 
which are expressed in spoken language. The child 
ought, when he writes, to be able to understand the 
meaning of what he is writing. Or, more correctly, he 
ought, in the main, in his writing, to be expressing 
ideas. Similarly, we now insist that when the child 
learns to read he shall be gaining the ability not merely 



68 PSYCHOLOGY OF COMMON BRANCHES 

to pronounce words, but to read a meaning into the 
words which he is pronouncing. 

Drill is necessary for the perfection of skill. This 
principle, that learning to write and learning to read 
should be related to each other and that both should 
be related to the spoken language of which they are 
the expression, should not be taken to mean that no 
drills should be given for the perfection of the ability 
to write or to recognize words. We have seen, in the 
case of writing, that it is often necessary to stop in the 
process of expression of thought and to take time to 
perfect the technique of form production or of the 
development of the proper movement. What is here 
meant is that writing and reading should always have 
a meaning for the child, but it is not intended to imply 
that this meaning should always be uppermost in his 
mind. There should, in fact, be times when the tech- 
nique of the production or of the understanding of 
words is the thing which is uppermost. If we attempt 
to develop skill merely as an incident to the recogni- 
tion of meaning, we find that there are large gaps in 
the child's ability. There are two extremes, then, 
which have to be avoided. On the one hand, the 
development of great technical ability which has no 
meaning or significance for the child and which there- 
fore cannot be used by him to serve its real purpose; 
and, on the other hand, the failure to develop the 
technique to such an extent that the acquisition may 
be used as an efficient tool by the child. 



READING 69 

Writing enhances the meaning of reading. A few 
remarks may be made here as to the manner in which 
reading and writing are related to each other. In the 
development of writing in the race, reading and writ- 
ing, of course, went together: that is, the race was able 
to recognize those signs which it could produce; and it 
could recognize only those which were produced be- 
cause it was dependent on writing for the creation of 
material to be read. The child, however, when he 
comes to read, is confronted by a large amount of 
material which has been developed in the past history 
of the race, the origin of which he is entirely unac- 
quainted with. A problem is then raised that may be 
put thus : Shall we introduce the child to this accumu- 
lated mass of printed matter as fast as he can learn to 
read it, or shall we repeat the history of the race and 
make writing keep pace with reading? It is not neces- 
sary to make the faster process of learning to recognize 
words keep pace with the slower process of learning to 
write them. When the child does learn to write, how- 
ever, it undoubtedly not only makes his perception of 
the letters more distinct, as we saw in the chapter on 
writing, but also gives him a better realization of the 
fact that in reading one receives a message from an- 
other person in the same way as in listening to another 
person talk. This fact furnishes an argument against 
deferring writing any longer than necessary. The con- 
nection between reading and writing may be empha- 
sized by relating both of them to oral expression. 



70 PSYCHOLOGY OF COMMON BRANCHES 

Writing and reading should be related to oral ex- 
pression. Both reading and writing may be related 
to oral expression in the following manner. The child 
or the class may be led to describe some experience 
they have had; this description may then be written 
out by the teacher and reproduced by the children, 
or written out by the children with the help of the 
teacher; and the children may then read what they 
themselves have composed, first orally, and later in 
« writing. When the connection between oral composi- 
tion, writing, and reading is thus made, the child comes 
to think of writing as having some use, as being a real 
activity, and related to the expression of his ideas 
instead of being merely a formal production of certain 
meaningless signs upon the paper. Similarly, reading 
comes to be the acquiring of ideas, or the gaining of' 
experiences from others rather than the ability to pro- 
nounce meaningless words. When reading and writing 
thus have acquired their normal meaning through 
their association with each other, the time is ripe for 
the development of a higher degree of technical skill 
in order that the ability may be gained to express and 
to recognize still more difficult ideas or ideas expressed 
in a more diflBcult form. 

The stages in learning to read 

Learning what printed words are for. Following this 
general account of the meaning and significance of 
reading and writing, we may describe the stages 



READING 71 

through which the child's recognition of words pro- 
gresses until it becomes complete in reading. In the 
first place, the child learns that printed words repre- 
sent spoken words. This knowledge may be gained 
before he is able to recognize any particular printed 
word as meaning any particular spoken word. The 
experience of seeing other persons read, the realization 
of the meaning of street signs, of store signs, etc., will 
give him this early type of recognition. The child 
comes to understand this without any special form of 
training, merely by casual observation of the actions 
of people about him. 

The word-learning stage. The child goes beyond 
this general recognition when he learns to connect 
certain words with the printed forms which repre- 
sent them. He may do this before he is able to read 
connectedly. He may, for example, recognize his own 
name when it is printed, or the names of the members 
of his family, or of familiar objects. This recognition 
gives him a starting-point for more coherent and con- 
nected reading. This association between the spoken 
name and the written word is really not much more 
complex or difficult than the connection of a spoken 
name with the object. It, of course, soon becomes very 
much more complex in virtue of the fact that different 
printed words are made up of combinations of the same 
letters, but at the start the child can associate a printed 
form with a name in very much the same way in which 
he associates the object with its name. The difficulty 



72 PSYCHOLOGY OF COMMON BRANCHES 

arises when the child begins to learn a large number of 
words. The amount of difference between different 
words is in many cases small, and it is necessary to pay 
a good deal of attention to the details of a word in 
order that it may be distinguished from one that is 
similar to it. 

The letters need not be learned first. This essential 
similarity between the association of a printed word 
with a spoken word, and the association of a name with 
an object, is taken advantage of in present-day meth- 
ods of teaching the child to learn to read. In the 
older methods it was assumed that the child had to 
be brought to this recognition by an indirect route; in 
other words, it was believed that it was necessary for 
the child first to learn the elements of which the word 
is composed, and then to be able to put them together 
into the word. The association was not between 
spoken word and printed word, but first between 
spoken names of letters and printed letters, then 
between the printed letters as they were combined 
into the word, and finally, by this indirect route, be- 
tween spoken and printed words. 

There are special difficulties in beginning with the 
names of letters or the sounds of letters. The matter 
was made still more complex by the fact that the let- 
ters which composed the words did not represent the 
sounds of the spoken language, but rather represented 
certain names which did not in many cases correspond 
with the sound. For example, in building up the word 



READING 73 

cat, the names of the letters c-a-t do not stand for the 
sounds of the spoken word, but are rather names 
which are more or less unrelated to the sound. This 
diflBculty was somewhat remedied when the sounds of 
letters were used instead of their names. The sounds 
of the successive letters represent in some measure the 
sound of the word as a whole, and the child can see 
that the combination of the letters as represented by 
their sounds represent the spoken word. Ey.en here, 
however, many difficulties arise in such a language as 
the English in which the spelling is not phonetic. In 
such a word as though, the combination of the sounds 
of the separate letters does not at all represent the 
sound of the spoken word. At the best, even if the 
language were entirely phonetic, there is no reason 
why it would be necessary to begin with the elements 
of which the words are composed. As has already been 
said, the child may form the direct associations be- 
tween the spoken and the printed word as the starting- 
point of his reading. 

The sentence is too complex to begin with. Some 
have attempted to go still further than this, and make 
the association first between a written sentence and 
the spoken sentence. This method seeks justification 
in the fact that an idea is commonly expressed by a 
combination of several words in a sentence rather than 
by a single word. In spite of this fact, however, the 
word is a fairly distinct unit of speech, and if we trace 
the development of speech in the child we find that 



74 PSYCHOLOGY OF COMMON BRANCHES 

he first isolates single words from the trains of sen- 
tences which he hears spoken by those about him. 
We found in our description of the language develop- 
ment of the child that he first uses sentence words. 
Single words represent for him trains of thought; and 
the supplementary parts of the idea are expressed 
through facial expression, gesture, etc. In learning to 
speak it is single words that first catch the child's 
attention, and the same is true in reading. The child 
may not be able to hold in his mind, at the beginning, 
the minor parts of a sentence and put them together 
into a sentence as a whole. We may, therefore, con- 
clude that his reading, as his speaking, should begin 
with words which form the core of a sentence or an 
expression of thought. After he has gained the ability 
to recognize a few important words, the others may 
then be introduced, and he will come gradually to the 
recognition of their meaning also. 

After the early stage letters and their sounds must 
be recognized. This gives the child the starting-point 
for the recognition of words. He will not progress far, 
however, until he understands that words which are 
printed represent spoken words, not because they are 
associated together in an arbitrary way, but because 
the printed word represents a combination of sounds 
in the same way that a spoken word represents a com- 
bination of sounds. In other words, he must come 
sooner or later, and in fact rather soon, to the under- 
standing of the principle of the alphabet. Although it 



READING 



75 



is not necessary for him to start with the recognition 
of the alphabet, yet it is necessary that he gain this 
recognition before he progresses far. 

Written symbols were originally pictures of objects. 
We may gain a clear idea of the meaning of the alpha- 
bet by a survey of the course of its evolution. At the 
beginning the writ- 



a' 



H 



Sun 





'0S 



Light 



ten signs which 
were used to ex- 
press ideas resem- 
bled the objects 

which they were ^ ]]\ ^ n Moon 

supposed to repre- 
sent. This is seen 
in picture-writing. 
Picture-writing, as 
the name indicates, 
conveys its mes- 
sage through a se- fig. 7. 
ries of pictures of ,,,, ^„„ „ ^, ^„^ 

^ (After E. B. Huey, Psychology and Pedagogy 

objects which when of Reading, with the permission of the pub- 
lishers.) 

put together sug- 
gest a connected story. Sometimes other signs, such 
as a rough map, are used to indicate the relations 
of the pictures to one another. The Chinese language 
still retains this same principle of picture-writing in 
that the signs which represent the words of the lan- 
guage were originally pictures of the objects. For 
example, the sun was represented by a circle with 



ILLUSTRATION OF PICTURE- 
WRITING 



76 PSYCHOLOGY OF COMMON BRANCHES 

a dot in the middle. (See Figure 7.) As it became 
easier to use straight Hues rather than curved hnes, 
another sign was substituted for this, but the meaning 
was still based on the original correspondence in 
appearance of the sign and the object. The Chinese 
language, then, instead of having twenty-six signs, as 
has our language, has thousands of signs representing 
individual objects or ideas, together with certain key- 
signs which may be used in combination with them. 

These pictures were then used to represent other 
objects having names of the same sound. The written 
language which we inherit, however, developed accord- 
ing to an entirely different principle. The develop- 
ment toward the 
new forms of print- 
ed signs probably 
had its origin in 
the necessity for 

Fig. 8, ILLUSTRATION OF PICTURE- writing prOpCT 

WRITING 
(After'B.B.llney, Psychology and Pedagogy Il^'DieS. A proper 

rihlrsf "^' "^'^^ ^""^ ^^'""'^^'"^ ""^ ^''^ ^''^" °^™^ cannot be 

expressed by the 
picture of the object which it represents, because the 
distinguishing marks of an individual are difficult to 
represent, and because it may be applied to a number 
of different persons. This led to the device of break- 
ing up the name into a number of parts each of which 
could be represented by some object. The name then 
was represented by a combination of the signs which 




READING 77 

represented other objects. See, for example, the sign 
which was used to represent the Aztec name, Itz-coatl. 
The first part of this name is the word for knife, and 
the second part, the word for snake. The name was 






7 "I A^ M 

Fig. 9. EVOLUTION OF M 

(From Judd's Genetic Psychology for Teachers [Appleton, 1903], p. 208.) 
" The figure shows tlie derivation of the letter M from the Egyptian 
hieroglyphic owl. The four forms in the upper part of the figure are 
Egyptian forms. The first form on the left of the lower series is an 
ancient Semitic form. Then follow in order an ancient Greek form, and 
two later Greek forms." (I. Taylor, in The Alphabet, pp. 9 and 10.) 

then represented, as shown in Figure 8, by a combi- 
nation of the picture of the knife and of a snake. 

The simplified pictures were finally used to repre- 
sent the first sound of a name. In early Egyptian and 
Phoenician times this process was carried a step farther 
by using the sign for a word, not to represent the word 
as a whole, but the first sound in the word. In this way 
there came to be developed a great many signs which 
stood for single sounds. Thus the letter M was devel- 



78 PSYCHOLOGY OF COMMON BRANCHES 

oped from the sign for the Egyptian word mulak (owl) 
through a series of steps illustrated in Figure 9. In 
many cases the same sound was represented by a 
variety of signs, because different words starting with 
the same sound might have signs to represent their 
initial sound. The Egyptians apparently did not 
develop a series of single signs to represent the various 
sounds. This was carried forward by the Phoenicians 
or the Greeks. 

Our alphabet does not entirely suit our language. 
As a result of this development we have a series of 
signs which stand for the sounds of the language. In 
the ancient Greek and Phoenician alphabets there was 
probably a complete correspondence between a series 
of sounds and of signs. In our own case, however, we 
have inherited an alphabet and have applied it to a 
language which is somewhat different from that for 
which the alphabet was devised. Therefore, we have 
some sounds which are represented by a number of 
letters, and some letters which represent a number 
of sounds. In other words, our language is not pho- 
netic. 

The child may make the association between the 
sound and the letter either by systematic drill or inci- 
dentally. To return to our description of the develop- 
ment of the child, we see that it becomes necessary for 
him sooner or later to awaken to a recognition of the 
sounds which are represented by the different letters. 
This may be done in two ways. In the first place, the 



READING 79 

child may be told what sound is represented by the 
letter; or, in the second place, he may be led to make 
an association between the sound of a letter by seeing 
the same letter appearing in a large number of words. 
We may call the first a definitely phonetic method of 
teaching, and the second an incidental method. 

A moderate amount of phonetic drill improves the 
ability to recognize words. Some amount of phonetic 
teaching is undoubtedly of value in helping the child 
both to analyze the spoken words into their sounds 
and to make the associations between the sound and 
the letter which it represents. This prevents a waste 
of time and leads to an earlier formation of the associa- 
tion than would occur if the association were made 
wholly by the incidental method. The need of making 
the association between the sound and the letter be- 
comes prominent when the child meets new words, 
but it is possible to develop such associations incident- 
ally, as is shown by the fact that the child who has 
had no phonetic drill may be able to recognize new 
words. But the phonetic drill may be carried to an 
extreme, and when this is done the child becomes 
expert in the recognition of the sound of words beyond 
the development in ability to recognize their meaning. 
There is some danger of overemphasizing the sounds of 
letters in contrast to the meaning of the words which 
they represent. 

An added difficulty is due to the fact of a lack of 
uniform correspondence between sounds and letters. 



80 PSYCHOLOGY OF COMMON BRANCHES 

In the English language, which is highly unphonetic 
in its spelling, the difficulty arises which has already 
been mentioned. A letter may represent one sound in 
one word and another sound in another word; and to 
teach that a letter represents a particular sound does 
not always enable the child to give it its appropriate 
sound in all words. Attempts have been made to over- 
come this difficulty by using additional signs to indi- 
cate when a letter is to be given one sound or another 
sound. These signs are called " diacritical marks." 
Other devices which have been used consist in the for- 
mation of a new alphabet, or in the invention of addi- 
tional letters to those of our alphabet in order to sup- 
ply this want. Whether or not diacritical marks or 
additional signs in the alphabet are used, we must 
recognize that they are for temporary rather than for 
permanent use. The child must ultimately come to 
recognize words which are printed in the ordinary let- 
ters in common use without diacritical marks. The 
question, then, is, whether he can better learn to 
recognize the various sounds of ordinary printed let- 
ters as they appear in different words by first using 
diacritical marks, or whether he can better learn by 
the incidental method. 

Diacritical marks should be used sparingly. It is 
undoubtedly true that we sometimes create difficulties 
for the child by calling them to his attention, and by 
the use of devices which have for their purpose the 
overcoming of these difficulties. The child may recog- 



READING 81 

nize the difference in the sound of a in say and in saw^ 
for example, without its presenting any particular 
difficulty to him. But if a diacritical mark is used in 
the one case, or in the other, or in both cases, he has 
an additional thing to learn. Undoubtedly some con- 
fusion in the mind of the child is inevitable, and the 
use of a few diacritical marks is desirable to overcome 
this confusion. A few years ago there was an extreme 
use of such signs and of new or artificial alphabets, but 
teachers are coming to discover that this extreme use 
of supplementary signs is unnecessary and serves to 
confuse rather than to help the child. Their chief use 
is to enable the child to gain the pronunciation of a 
word which is new to him in his reading and in his 
speech, by consulting the dictionary. This need does 
not arise in the early years. 

Spelling necessitates a clear recognition of the let- 
ters. The necessity for the recognition of the letters 
as the elements of a word is due also to the require- 
ments of writing. When a person writes words he 
must know not merely the general form of the word 
or the more prominent letters which compose it, but 
he must be able also to give each individual letter in 
its proper order. The requirement of spelling necessi- 
tates more minute analysis of the word than the re- 
quirement of its recognition. Furthermore, it has 
been shown by the photographic method that the child 
makes many more eye movements even in the recogni- 
tion of words than does the adult. The child in the 



82 PSYCHOLOGY OF COMMON BRANCHES 

first two or three grades moves the eye almost as many 
times as there are letters in the word; whereas the 
adult, as we shall see later, makes only four or five 
pauses in an ordinary line of print. This is an indica- 
tion that the child does not recognize words as wholes 
to the same degree as does the adult, even though he 
has been taught by the word method. On the score, 
then, of the recognition of words and of the ability to 
spell words in writing, it is necessary that the child 
should finally get a clear recognition of the letters 
themselves, and not merely of the words as wholes. 

To read sentences fluently requires the develop- 
ment of eye-movement habits. The ability to read is, 
in addition to the ability to recognize words, the abil- 
ity to recognize them rapidly and connectedly as they 
appear in their order in the sentence. The sentence 
consists in a combination of words which express a 
coherent meaning. When the adult reads he takes in 
during each of a series of eye pauses a group of letters 
which make up a word, several words, or even phrases, 
at the same time. The mechanism by which this 
recognition of successive words and phrases take place 
has been recently studied. The opinion was previously 
held that the eye travels steadily along the line and 
that the words are recognized while the eye is moving. 
Experiments which have recorded accurately the 
movements of the eye have shown that what really 
takes place is a series of rapid movements separated 
by eye pauses, and that the recognition of the word 



READING 83 

takes place during the eye pauses. The number and 
length of these pauses vary with different persons and 
in the same person with different kinds of subject- 
matter or with different sizes of type and length of 
lines, etc., but it is fairly constant for the same person 
under the same conditions. Each person has devel- 
oped a certain habit of eye movement which accords 
with his habits of reading, or which expresses the 
habits of recognition which he has formed. It is a 
question whether the eye movement is the factor which 
determines the kind of a person's recognition, or 
whether the eye movement is governed by the recog- 
nition of meaning; but at any rate it is clear that one 
of the necessities which confronts the child as he learns 
to read is the necessity of building up these eye- 
movement habits. 

Progress consists in a decrease in the number of 
movements and an increase in the scope of recognition 
at each pause. As was mentioned previously, it has 
been discovered that with the very young child these 
habits of recognition of words, or large parts of words 
at a time, has not yet been completely formed. The 
child makes progress in the development of the habit 
from the stage in which he makes a large number of 
movements, corresponding to the individual letters or 
small groups of letters, to the stage in which he makes 
fewer movements corresponding to larger groups of 
letters or words. Recent experiments indicate that 
probably by the third grade, many if not most of the 



84 PSYCHOLOGY OF COMMON BRANCHES 

children have developed these movement habits 
sufficiently to read with a high degree of rapidity. 

Words are connected into sentences by inner speech. 
These facts in regard to eye movements throw light 
upon what happens in order that we may recognize 
words in reading. Evidently what we get of the printed 
page is a series of glimpses. We are not aware of these 
pauses in our reading, and in fact we are not aware 
that we perceive the sentences of a page piecemeal, 
but it seems rather as though we read continuously. 
The reason for this is that as we perceive the words 
we put them together and weave them into a whole as 
though we were speaking the sentences. Words are 
connected in our minds in the first place through 
speaking them in sentences and through listening to 
others speak. When we read there is a tendency also 
to repeat the sentence. With unpracticed readers this 
is carried to such an extent that they move their lips 
in the pronunciation of the words that are being read. 
Even though a practiced reader does not give these 
outward signs of pronunciation, yet it has been shown 
by experiment that the vocal cords and the tongue 
make very slight movements which correspond to the 
words which are being read. The glimpses which are 
got of the line in reading, then, serve to set up the 
train of activities which correspond to the speaking of 
the sentence. 

Inflection, pitch, and tone quality correspond to the 
meaning of the sentence as a whole. Not only are the 



READING 85 

words reproduced in some form of inner pronuncia- 
tion accompanied by the imagination of the sound of 
the words or of the feeling which is produced in pro- 
nouncing them, but we also have imagery which cor- 
responds to the relationships of the words in the sen- 
tence. When we speak a sentence the words are not 
pronounced in a monotone, but they are given a cer- 
tain emphasis and inflection which is due to their 
relationship to the other words, independent of their 
character as words taken separately. If we listen to 
a person talking in another room, although we cannot 
distinguish the words, we have some notion of the type 
of sentence which he is uttering. We can distinguish 
between a question, a declaration, and an exclamation, 
etc. In a similar way the pitch and quality of the voice 
represent the emotion which accompanies the words 
as they are being articulated. Although one may, 
when he has acquired the habit of rapid silent reading, 
slur over the articulation of the individual words, yet 
this modulation of the voice remains, and is repre- 
sented in the imagination or in actual changes in the 
vocal cords or in the other organs of speech which 
correspond to such modulation. These tendencies to 
inner speech are somewhat different from those which 
complete themselves when one is actually speaking, 
as is shown by the fact that they may take place dur- 
ing inspiration of breath as well as during expiration; 
but though they are thus modified in silent reading, 
they have an important connection with the appre- 
hension of meaning. 



86 PSYCHOLOGY OF COMMON BRANCHES 

Inner articulation is more important in some kinds 
of reading than in others. The importance of inner 
articulation varies with the rapidity of the reading; 
or with reference to the aim, according as it is merely 
the rapid apprehension of meaning or some other form 
of appreciation of what is being read. When one is 
reading passages the value of which depends upon the 
sound quality, it becomes necessary to read in such a 
way that this sound quality will be recognized. In 
poetry, for example, where the rhythm and the melody 
and the alliteration, or other sound characteristics, are 
important in the appreciation of the sesthetic qualities 
of the poem, it is necessary to read in such a way that 
one has time to get a clear experience of these char- 
acteristics in the imagination. The same thing may 
be true to some extent of literary prose. It is, however, 
not correct to apply the principles which govern such 
forms of reading to reading of all sorts. It is undesir- 
able in much of our reading, which is so voluminous 
that the meaning must be apprehended as rapidly as 
possible, to dwell upon these elements of the sentence. 
It is not necessary in a great many cases to pay partic- 
ular attention to every detail which is being read, but 
it is desirable to gather only the main ideas. 

Oral and silent reading 

Ability in silent reading is much more important 
than in oral reading. This raises the whole question of 
oral and silent reading, which must be considered 



READING 87 

before we finally arrive at a conclusion with reference 
to rapid reading. Traditionally the reading in the 
schools has been chiefly oral reading, and little or no 
attention has been paid to silent reading, or to reading 
for the purpose primarily of getting the thought, and 
not for the purpose of expressing it to others. The 
relative value of these two sorts of reading must be 
considered in reference to the use to which they will 
be put in the child's after life. From this point of view 
it is clear that silent reading is by far the more impor- 
tant. Oral reading is the merest incident in the life of 
the average adult; whereas silent reading plays a very 
important part in his life. The only justification for a 
comparatively large amount of emphasis upon oral 
reading would be the assumption that it is a necessary 
condition for the proper development of oral reading. 
Proficiency in silent reading does not correspond 
closely to proficiency in oral reading. One may hold 
that while oral reading is not to be used, yet it is neces- 
sary to the development of silent reading. If we com- 
pare the oral and silent reading of the adult, however, 
we are led to believe that there is quite a wide differ- 
ence between the two processes. If the adult who has 
become practiced in silent reading is required to read 
orally, he will see that the apprehension of meaning is 
less perfect than when he does not pronounce the words 
aloud. The oral reading, then, is to some extent 
an interference with the apprehension of meaning. 
Furthermore, it is evident upon the briefest observa- 



88 PSYCHOLOGY OF COMMON BRANCHES 

tion that a child may read orally and pronounce the 
words with a fair degree of accuracy of inflection, etc., 
and yet have very little comprehension of what he is 
reading. 

Oral reading is of little value for silent reading after 
the early stages of learning. We must assume, there- 
fore, that, although there is inner pronunciation in 
silent reading, yet the development of silent reading is 
mainly to be got by the suppression to a large extent 
of the oral accompaniment, and the fixing of attention 
on what is being read. Experiments in which the child 
is encouraged to get the meaning from the printed 
page rapidly and without pronunciation, or at least 
without oral reading, indicate that he is capable of a 
much higher degree of development in this direction 
than we have been accustomed to think. Oral reading 
is doubtless the natural and best kind of reading for 
the beginner and perhaps during the first year. It 
furnishes the most natural motive for the child to get 
the meaning of the printed words, and his rate of 
recognition is still so low that it cannot be retarded by 
speaking. Aside from this early reading, however, 
oral reading is chiefly of value, not because of its 
bearing on the greater part of our silent reading, but 
because it is of itself of importance in the development 
of oral expression, and because it leads to an ap- 
preciation of the aesthetic qualities of certain types of 
material. 



READING 89 

Efficiency in reading 

Efficiency is measured by speed and apprehension 
of meaning. We have assumed that the chief purpose 
of reading in the schools is to develop eflSciency in 
silent reading. This assumption is entirely justified 
by the use to which reading is put in after life. If this is 
true the question next arises: In what does efficiency 
consist? Undoubtedly one element in efficiency is 
speed, and this has been incidentally referred to. 
Rapid reading, however, is of little importance unless 
the meaning is apprehended with clearness and ac- 
curacy. We must include, then, the ability to repro- 
duce or to use what has been read, as well as the 
amount which has been read, in our measure of effi- 
ciency. The speed is easily measured by measuring 
the amount that a person can read in a given time. 
The degree to which the meaning is apprehended may 
be measured in several ways. The pupil may be re- 
quired to give an account of what he has read; or he 
may be asked to answer questions on the material 
which he has read. These are the tests which are com- 
monly used, and when they have been applied, it has 
been found that the rapid readers apprehend the 
meaning about as well as slow readers. Furthermore, 
when a person through a course of drill increases his 
speed in reading, he is as likely to increase the ac- 
curacy with which he apprehends the meaning as the 
reverse. In fact, the increased speed of reading often 



90 PSYCHOLOGY OF COMMON BRANCHES 

seems to heighten the attention or to increase the 
amount of mental energy which is expended, and this 
is expressed in the better apprehension of meaning as 
well as in greater speed. The figures in Table I show 
that the speed of reading in the lower grades may be 
greatly increased, and that this may be accompanied 

TABLE I 

Improvement in reading from September to March^ 





Rate in 
words per 
minute 


Amount 
reproduced 


Percentage of 

correct answers 

to questions 


Grade 3 

September 


76.4 
149.1 

72.7 

92.7 

163.3 

70.2 

113. 
129.2 
16.2 

128. 
130.1 
2.1 

122.7 

142.8 

21.8 

147.2 

158.9 

11.7 


71.1 
135. 
63.9 

133.8 

212.9 

79.1 

52.2 
70.5 
18.3 

52.1 
85.3 
33.7 

75.6 

125.5 

49.9 

116.5 

179.6 

63.1 


44 6 


March 


44 


Per cent gain 


Q 


Grade 4 

September 


56 7 


March 


60 9 


Per cent gain 


6 6 


Grade 5 

September 


16 3 


March 


25 6 


Per cent gain 


98 


Grade 6 
September 


27 1 


March 


35 


Per cent gain 


8 


Grade 7 

September 


42 7 


March 


48 3 


Per cent gain 


5 6 


Grade 8 
September 


55 3 


March 


62 5 


Per cent gain 


7 1 







1 From an unpubUshed master's thesis by K. D. Waldo, on file 
in the hbrary of the University of Chicago. 



READING 91 

by an increase in the ability to apprehend the mean- 
ing. 

Rate of reading is not so important in the compre- 
hension of difficult matter as in easy reading. There 
is another element in efficiency which is not accurately 
measured by the means which have been mentioned, 
namely, the ability to relate what is read to one's past 
thinking, or to examine it critically in order that one 
may judge of the correctness or worth of what is read. 
In some kinds of reading, also, it is necessary to spend 
considerable time in order that the thought may be 
apprehended. The tests which have been used have 
referred chiefly to the types of reading-matter which 
can be readily apprehended without stopping to think 
through the ideas which have been expressed. It is 
very likely that some modification will have to be 
made in the conclusion with reference to rapid reading 
when the other sort of test is made, and when different 
kinds of reading-matter are studied. For example, in 
solving problems in arithmetic or in other forms of 
mathematics, much of the accuracy, or much of the 
efiiciency, depends upon the ability to grasp the mean- 
ing of the problem as expressed in its statement. This 
is one form of reading, and it must be included in 
any comprehensive view of what efficiency in reading 
means. 

The rate of ordinary reading is usually too slow. 
Even with this qualification, however, it must be said 
that there is ample evidence that the majority of per- 



92 PSYCHOLOGY OF COMMON BRANCHES 

sons read very much more slowly than is necessary. 
The reading rate has probably been fixed largely by 
the speed in oral reading, and this is one reason why 
it is undesirable to overemphasize oral reading in the 
schools. A little effort on the part of adults is sufficient 
very materially to increase the rate of reading and the 
experiments which have been made indicate that chil- 
dren are also susceptible to this type of training. 

Speed must be flexible. As was hinted in a previous 
paragraph, the child must be taught to read each par- 
ticular kind of subject-matter with its appropriate 
speed. In other words, he must read only as rapidly 
as he can grasp the thought. The test which was made 
in one school showed that the sixth grade and the sev- 
enth grade read the same passage with about the same 
degree of speed, but the sixth grade was able to appre- 
hend only a very small proportion of the ideas of the 
passage. These sixth-grade pupils had not had the 
proper training, or at least did not have the proper 
attitude in this particular test. They should have 
realized that they were not getting the meaning, and 
they should have adjusted their speed of reading 
accordingly. With some kinds of subject-matter it is 
necessary that one learn to skim through and gain 
merely a general notion of the thought which is 
expressed. The newspapers, for example, furnish a 
great deal of material which should be read in this 
manner. When one has only learned to read carefully 
word by word, he either has not the ability to go over 



READING 93 

the amount of reading-matter which may advantage- 
ously be read by the average educated adult at the pre- 
sent time; or if he does, he expends very much more 
time than should be spent. 

Rate of reading is increased by attending to the 
meaning as distinguished from the mechanics. It is 
not known with certainty what change takes place in 
a person's reading habits when he increases his speed 
of reading. Some change in eye movement must, of 
course, take place. Either the movements are less fre- 
quent, that is, fewer pauses are made to the line, or the 
duration of each pause is less, or both of these factors 
change together. If we compare rapid and slow read- 
ers, we find that some rapid readers owe their abihty 
to the fact that they make their pauses of short dura- 
tion, and others to the fact that they make few pauses 
to the line. This, therefore, does not give an answer 
to our question. Dearborn found that a reader tends 
to fall into a set habit of eye movements in reading a 
certain passage of a particular length of line, size of 
type, etc., and concluded that the habit was a more 
or less accidental thing and that the speed was deter- 
mined to a large extent by the eye-movement habit. 
On the other hand, the experience of those who in- 
crease the rate of their reading indicates that they do it 
chiefly by paying attention to the apprehension of 
meaning. They attempt to fix their attention on the 
things which are read about, and to pay little attention 
to the mechanics of the reading itself. The suppression 



94 PSYCHOLOGY OF COMMON BRANCHES 

of lip movement and of the images of the sound of the 
word or of the pronunciation of the word assists in 
rapid reading. When a person is thinking of each 
word and hears it distinctly or feels how it is pro- 
nounced, he can only read at a certain limited rate. 
When the word, on the other hand, suggests certain 
ideas, or images of things, and the reader frees himself 
from the images connected with the word itself, he is 
enabled to read more rapidly. 

The variation in speed according to the subject- 
matter shows the importance of apprehension of 
meaning. The conclusion that rapidity of meaning 
depends more upon the ability to apprehend the mean- 
ing quickly than upon the habit of eye movement is 
further confirmed by the fact that the rate of reading 
varies considerably with the kind of subject-matter. 
If the same person is tested in easy narrative and in 
more difficult scientific exposition, it will be found that 
he reads the former more rapidly than the latter. The 
eye movements in the two passages would not be af- 
fected by the difference in the subject-matter, and 
therefore we must conclude that they are not the pre- 
dominant elements in determining speed. 

The pupils should be trained in the rapid apprehen- 
sion of meaning. If this conclusion is correct, the 
training of the pupil in rapid reading can be brought 
about best by some means which will call his attention 
to the meaning rather than to the mechanics of the 
reading. It is found that merely to urge the pupil to 



READING 95 

read rapidly is an effective way of increasing his speed. 
Any motive which will lead him to desire to get the 
meaning quickly will be an effective one. This will at 
the same time avoid the danger of the pupil increasing 
the rate of his eye movements or of the pronunciation 
of words without increasing his rate of apprehension, 
so that the pupil tends to read in a mechanical fashion. 
There are a number of devices which might be used to 
assist the pupil in getting the meaning. Catch pas- 
sages are sometimes used in which some absurdity is 
hidden, and the pupil is directed to detect the absurd- 
ity as rapidly as possible. Another means is to have 
the pupil give a summary of what he has read, at the 
same time trying to read rapidly; or to direct him to 
read a passage for the sake of getting at some point or 
the answer to some question which is given before- 
hand. 

Improvement with age above the fourth grade is in 
ability to grasp more difficult subject-matter. The 
conclusion that the rate of reading is connected more 
closely with apprehension of meaning than with the 
mechanics of reading is also indicated by the fact that 
when pupils of different grades are given material 
which is suited to their thought, those who are in any 
grade above the fourth can read with about the same 
degree of rapidity. That is, by the time the pupil 
reaches the fourth grade the mechanics of reading are 
sufficiently developed so that he can read rapidly any- 
thing that he can understand. If, however, the lower- 



96 PSYCHOLOGY OF COMMON BRANCHES 



grade pupil is given a passage which is suited in subject- 
matter to a higher-grade pupil, the rate of his reading 
as well as the accuracy of his understanding usually 
drops. In the apprehension of meaning, as well as in 
the speed of reading, there is a great deal of over- 
lapping among children of successive grades One in- 
vestigation, for instance, indicated that 42.6 per cent 
of the children of the fifth grade surpassed the average 
of the sixth grade in rate of reading. (See Table II.) 









TABLE 


II 










Percentage of children in lower grades exceeding the average 


performance of children in higher grades in the same test ^ 




Rate 


Words reproduced 


Percentage 




6 


7 


8 


6 


7 


8 


6 


7 


8 


Fifth .... 


42.6 


36.1 


29.5 


24.6 


8.2 





26.2 


13.1 





Sixth .... 


— 


35.5 


29.4 


— 


15.7 


2 


— 


15.7 


4 


Seventh . . 


— 


— 


27.7 


— 


— 


14.8 


— 


— 


24.1 



In reading as in writing the proper relation must be 
kept between mechanics and meaning. The process 
of learning to read illustrates very much the same 
principles of learning as does learning to write. In the 
first place, the child has to master certain mechanics 
in order that he may be able to gather meaning from 
the words on the printed page. In the case of writing, 
the problem is to master the mechanics of expression 
» From K. D. Waldo. 



READING 97 

so that a meaning which is represented in the mind of 
the child will be expressed. In both cases the aim is 
either the expression or the understanding of meaning. 
When the final development is reached the mechanics 
will fall out of attention, but for a time it is necessary 
that the mechanics be perfected in order that they 
may serve as an efficient medium for the recognition 
or the expression of meaning. In both cases the me- 
chanics may be too much neglected, or the attention 
may be retained upon them too long. Efficient teach- 
ing of reading, as of writing, consists in paying just 
enough attention to the mechanics to make of them a 
tool for the apprehension of meaning, but to give no 
more time and energy to their development than is 
necessary to serve this end. 

REFERENCES 

1. W. F. Dearborn: Psychology of Reading. Columbia University 
Contributions to Philosophy and Psychology, vol. 14, no. 1. 

2. E. B. Huey: The Psychology and Pedagogy of Reading. Mac- 
millan. 1908. 

8. C. H. Judd: Genetic Psychology for Teachers. Appleton (1903), 
chap. VIII. 

4. K. D. Waldo: "Tests in Reading in the Sycamore Schools." 
Elementary School Journal (1915), vol. 15, pp. 251-68. 

5. F. Jenkins : Reading in the Primary Grades. Houghton Mifflin 
Company. 1913. 



CHAPTER V 

MUSIC: PERCEPTUAL LEARNING 

The chapter deals with the process of learning to 
read music. We shall consider in this chapter chiefly 
the ability to read music as shown by the ability to 
sing a melody from the printed score. We shall as- 
sume that the child has learned to sing in a simple 
fashion before he is to be taught to read. This neglects 
the earlier phase of learning to recognize and sing 
tunes from having heard them, but in the main we 
shall assume that the child has learned to sing simple 
tunes just as we assumed in our discussion of reading 
that he had learned to speak. There are several con- 
siderations which justify this apparent neglect of the 
method by which the child learns to sing from ear, in 
favor of a description of the method by which he learns 
to read music. He learns to sing by ear by the simple 
method of imitation, and there is not much of tech- 
nique in the process. This is shown by the fact that 
many children can follow a tune before they go to 
school. Furthermore, the general principles of music 
which are represented in singing by ear will be brought 
out in the description of singing by note. Finally, the 
importance of beginning the reading of music early in 
the grades is being more and more recognized, so that 



MUSIC 99 

now in many places the child learns to read music 
almost as quickly as he learns to read printed matter. 
Reading simple melodies is comparable in difficulty 
to reading printed language, but reading music has 
been deferred in traditional school practice because of 
convention and tradition, and not because it was so 
inherently difficult as to make this postponement 
necessary. 

The enjoyment of music is not treated in this chap- 
ter, because, although this is one of the chief aims of 
education in music, it is reached indirectly, and it is 
the intellectual phase of learning music which is sub- 
ject to analysis. 

The child must first be able to carry a tune. Learn- 
ing to read music, as has been said, presupposes that 
a person is able to distinguish different tones, — or in 
technical language that he can distinguish tones of dif- 
ferent pitch, — and that he is able to carry a series of 
tones in mind to form a melody. The ability to read 
is, as in the case of reading words, the ability to make 
the association between a series of printed notes and a 
series of tones. One cannot connect the notes with the 
tones unless the tones are already recognized. The 
child, before he begins to read music, then, must have 
had some training in the ability to carry a tune. This 
training may take place in the kindergarten or in the 
first grade or two, or even before this time. Many 
children learn to carry simple tunes before they even 
enter the kindergarten. 



100 PSYCHOLOGY OF COMMON BRANCHES 

The recognition of intervals and melody 

Reading is the recognition of the relationship of 
tones and not of separate, individual tones. The recog- 
nition that the printed score stands for music which is 
heard or which is sung, as in the case of reading, is one 
that the child gets merely by seeing music used. After 
the pupil has learned that the notes on the score repre- 
sent melodies, the next step is to be able to associate 
certain particular notes, or rather certain connected 
series of notes, with a particular melody. The recog- 
nition of series or sequences of notes, and the corre- 
spondence between these and the sequence of tones in 
a melody takes place, not through the association of 
the pitch of the individual notes on the scale with the 
pitch of the individual notes which are sung, but 
rather through the recognition of the relationships of 
different notes to one another. The recognition of the 
relation of single notes to single tones makes possible 
the ability to tell absolute pitch, which is a relatively 
infrequent sort of ability. Very few persons can tell 
when a note is struck on the piano what note on the 
scale it is. The ability can be developed by training 
and is the refinement of the ability which the moder- 
ately trained person possesses of telling roughly the 
pitch of a tone. The method of identifying a tone 
which most persons pursue is first to have a basic pitch 
given and then relate other tones to this one. 

The recognition of intervals is distinct from the 



MUSIC 101 

recognition of individual tones. The pupil learns 
through practice to associate the interval between 
two notes on the printed score with an interval in the 
tones as he sounds them or hears them sounded by 
somebody else. When the pupil reads the interval 

C-E 



"^ ^ jij he can sing it, not because he 



carries in mind the pitch of the two notes separately, 
but because he carries in mind the difference in pitch 
which is represented by the combination. The tone 
which is sounded as C may be any tone whatever and 
may not correspond to a tone which represents C on 
any instrument. But whatever tone is chosen for C, 
the interval between C and E is always recognized as 
the same. 

In learning to read, the child becomes familiar with 
the various intervals of the scale. When the ability to 
recognize the intervals between notes is completed, 
the pupil can reproduce or name all the intervals on 
the scale. This includes the intervals between adja- 
cent notes as well as the notes which are separated by 
one or more intervening notes. Let us pause a moment 
to see what this means. If we consider merely adjacent 
notes, it means that two of the intervals are recognized 
as being but half as great as the other five. These two 
intervals are designated \ in the accompanying figure 



g-^-^^^..,...z^K:^|-^^-(^^|---=gI^ 



102 PSYCHOLOGY OF COMMON BRANCHES 

and the rest are designated 1. These smaller intervals 
are sometimes called half steps and the larger ones 
whole steps. The wider intervals than those between 
adjacent notes are also affected by the existence of the 
half steps. Thus the interval C-E is not the same as 
the interval D-F. We may summarize these facts in 
the statement that our music is written in a certain 
conventional scale/ and that the pupil has to learn 
to read melodies in terms of this scale. This makes 
learning to read music a more complicated matter 
than it would be if the intervals between adjacent 
tones of the scale were all equal. The child, of course, 
is prepared to recognize the intervals of the scale be- 
cause of the fact that he has already become familiar 
with it by ear, and he does not first learn them by cal- 
culating that an interval is made up of so many whole 
steps or half steps. Still, if the scale which the child 
first learned by ear were made up of equal steps, the 
recognition of various intervals on the printed scale 
would undoubtedly be easier. 

The child should learn to read simple music before 
receiving formal instruction in the scale. The instruc- 
tion of the child might be begun, as it has sometimes 
been begun in the past, by the attempt to teach the 
child in a formal manner the intervals of the scale. 
This, however, is not necessary. The child acquires 
sufficient familiarity with the intervals of the scale 

^ Only the major scale is considered here for the sake of simplicity. 
The same principle applies to the minor scales. 



MUSIC 103 

to enable him to sing, without knowing the names of 
the notes, without practice in striking intervals, or 
even in running scales. The child may go further than 
this and learn to read simple music and strike the inter- 
vals which he meets in it by becoming familiar in an 
incidental manner with all the possible intervals which 
are to be found. 

Formal instruction should later supplement reading. 
While it is true that the child should not begin with a 
formal study of the scale and its intervals and with 
drill in reproducing intervals which are represented on 
a printed score, it is equally true that some formal 
study is desirable as soon as the child has gained suffi- 
cient mental maturity and has learned actually to use 
the scale with some ease. The explanation of the whole 
steps and half steps and the drill in striking intervals 
quickly and accurately, which before the child has 
learned to read at all is a dull and almost fruitless 
grind, at its proper time clarifies his recognition of the 
intervals of music. There is no scientific evidence at 
hand to enable us to say just when this formal instruc- 
tion should be given, but on the basis of the general 
principles of the child's mental development it should 
probably begin at nine or ten years of age. 

A difficulty is caused by the use of different keys. 
We have thus far assumed that musical compositions 
are always written with the keynote at the same place 
on the staff. This, of course, is not true. It is often 
necessary for various reasons — for example, to adapt 



104 PSYCHOLOGY OF COMMON BRANCHES 

a song to the pitch of a voice or to harmonize several 
instruments — to shift the pitch of the keynote and 
the whole piece up or down. Each position on the 
printed staff represents (within slight variations) a 
fixed and definite pitch. The only way in which a 
piece can be written in a different key from the one 
we have assumed as a standard — the key of C — is 
to place the keynote at a different point on the staff. 
This would not create so much difficulty if the inter- 
vals of the scale were all equal, but since they are not 
equal, it is necessary, when the keynote of a piece is 
shifted, to modify the pitch which is represented by 
some of the lines or spaces. Otherwise the whole and 
half steps would not come at the right place in the 
scale. The modifications consist in shifting the pitch 
of certain notes up or down a half step. A sharp (tf) 
means a shift upward and a flat (t>), a shift downward. 
We may illustrate by indicating the shifts which must 
be made when the keynote is D instead of C : — 



^e^^ 



* 



-ZS-&- 



o ^ - 



Formal instruction should follow the first practice in 
reading. Here again the child might be taught the 
differences between different keys in a formal manner, 
and this method was formerly pursued, with the con- 
sequence that it was made so difficult that the young 
child could not learn it. All that is necessary at the 
beginning is that the child become accustomed to sing- 



MUSIC 105 

ing in different keys and that he learn to recognize the 
basic notes in a particular key as being situated on a 
particular line or space. A device^ for helping to recog- 
nize where the keynote is situated is used in a series of 
books published by C. H. Congdon. In these books in 
the earlier melodies of a new key, the space or line 
upon which the keynote is situated is indicated by a 
faint orange line. The use of this method, whether or 
not accompanied by some such device, does not make 
the learning a perfectly simple affair, it is true, but it 
makes it very much easier for the child than it would 
be to enter into an elaborate explanation of the theory 
of the matter. In the case of different keys as in the 
case of the scale itself, formal instruction is necessary 
in order to complete the crude recognition which is 
gained without it. The time at which this instruction 
should be given is doubtless to be determined by the 
time when the child grasps clearly the fundamental 
characteristics of the scale. 

Only formal instruction begins with the key of C. 
The key of C has been taken as a starting-point for 
convenience of description in this discussion, but it 
should not be inferred that the child is to begin his 
singing or reading in this key. The starting-point in 
the practice of reading or singing should be at the key 
or keys which suit the pitch of the child's voice. The 
starting-point in the formal instruction, as in this dis- 
cussion, may be the key of C. 

^ This device is practicable only in the use of simple melodies in 
which there is no change of key, or modulation. 



106 PSYCHOLOGY OF COMMON BRANCHES 

Rhythm 

The most fundamental element in music is rhythm. 
We have taken melody — that is, the sequence of 
tones — as the first element of music to be mentioned, 
because it is the one which most readily attracts the 
attention and the representation of which is most 
prominent. As a matter of fact, however, melody is 
not the fundamental element of music. There is an- 
other element that precedes it in racial development 
and also in the development of the child. This is the 
element of rhythm. Music may in fact be regarded as 
a specialization of the rhythmical activities. Rhythm 
is used in a great variety of forms of action besides 
music. The music which is characteristic of primitive 
peoples consists chiefly of rhythm as illustrated in 
their drum-beating. Rhythm also is characteristic of 
many of our actions which we do not think of as at all 
related to music. Many forms of work are carried on 
in rhythm and can be done with the most economical 
expenditure of energy in this way. Many of the physio- 
logical processes, such as the heart-beat and breathing, 
are rhythmical in their nature. Speech itself is rhyth- 
mical, and this may be verified both in prose and 
poetry. In the case of music, the rhythm is somewhat 
more regular and is connected with the elements of 
pitch and tone. 

Rhythm consists in the regular recurrence of acts 
divided into groups. In a rhythmical activity, such as 



MUSIC 107 

music or dancing, the individual acts which compose 
the entire chain of acts follow one another at regular 
intervals and are also arranged in groups each contain- 
ing, in the simpler cases, a uniform number of single 
acts. Marching is a simple illustration. Each step 
represents the single element, and each step takes the 
same amount of time as every other step. These single 
steps are usually put into groups of two each by accent- 
ing by a drumbeat or the voice every other step, 
commonly each step of the left foot. The rhythm be- 
comes more complex in dancing, but it can always be 
analyzed into these two elements, the regular succes- 
sion of a series of steps or movements and the divi- 
sion of the series into groups. 

Music has developed out of dancing. This illustra- 
tion suggests the relation which dancing holds to 
music. Dancing was the more primitive form of expres- 
sion and was developed as a part of the religious cere- 
monies of primitive people. In order to unify the danc- 
ing of a group of people and to intensify and emphasize 
the feeling of rhythm, the dance was accompanied by 
the beating on the drum and monotonous singing. In 
order to furnish more varied accompaniment, musical 
instruments were gradually developed and the songs 
gradually acquired more definite and complex melody. 

Training in rhythmical movements prepares for mu- 
sic. It is necessary to recognize the fact that rhythm 
has a deeper seat than the music which is sung or 
played on an instrument. Rhythm which is only kept 



108 PSYCHOLOGY OF COMMON BRANCHES 

by following the beat of some time-marker, such as 
the metronome, must always be mechanical, formal, 
and artificial. To be a significant form of expression 
rhythm must be felt, and it is felt when the whole body 
responds, and does in fact move in harmony with the 
tempo of the music. This makes it clear that a com- 
plete training in music must go back to the training 
in rhythmical bodily movements. The training in 
dancing, of the type which is being introduced into the 
schools, is not only of value to secure bodily control 
and poise, therefore, but is also a valuable introduc- 
tion to the appreciation of music. 

Rhythm is represented by notes and bars. While 
the pitch of the tones is represented by the position of 
the notes on the staff, the rhythm is represented by 
appropriate signs, and the child has to learn to inter- 
pret these. The duration of a tone is represented by 
the kind of note which is used, and the length of each 
unit group of notes is indicated by the division into 
measures. The pupil has to learn to recognize the 
type of rhythm which is represented in the different 
kinds of time — two part, three part, four part, etc. ; 
to hold the tones the length of time indicated by the 
notes, at the same time fitting them into the rhythm; 
and to indicate the divisions between measures, or 
the lesser divisions between parts of measures, by 
accent. 

Formal instruction in tempo and its representation 
should come after some reading ability is gained. A 



MUSIC 109 

child may learn to give the proper duration to the 
various notes, and to give the accent at the proper 
place in the measure, and to associate these with the 
aspects of the printed score which represents them, in 
the same way in which he learns the meaning of the 
different tones in a melody. He learns to associate the 
elements of rhythm with the characteristics of the 
score which represents them at first by the incidental 
method. It becomes necessary in the course of time to 
call his attention particularly to these facts and to 
give him a clear idea of their meaning. Here again 
the ability fully to understand the complexities of the 
elements of music and their representation need not 
be developed before some ability in reading has been 
gained. 

Harmcmy 

Harmony rests on the recognition of consonance and 
dissonance. There is still a third characteristic in 
highly developed music which the child can appreciate 
to a greater or less extent, but which is not so funda- 
mental as those of melody and rhythm. This char- 
acteristic is harmony. Certain tones, when sounded 
together, give persons who have a sense for mu- 
sical harmony a pleasurable experience. Others when 
sounded together produce displeasure. The psychol- 
ogy of harmony and disharmony is not entirely clear. 
All we know is that, for most persons, certain combina- 
tions are pleasing and others are not. Some combina- 



no PSYCHOLOGY OF COMMON BRANCHES 

tions also are more pleasing than others. Among those 
which are pleasing we recognize different degrees of 
harmony. The octave, for example, is recognized as a 
combination in which there is almost complete fusion 
of the two tones. Certain other intervals — for ex- 
ample, those which are separated by four steps or by 
three steps, as the combination C and G, or C and F — 
make what is called " perfect consonance," because 
no disharmony appears when they are sounded to- 
gether. Others separated by intervals of two steps, as 
C and E, or E and G, make what is called " imperfect 
consonance," because some disharmony is felt when 
these chords are sounded. It is not necessary to go 
into the various psychological theories which have 
been offered to explain the difference between har- 
mony and disharmony, particularly since the whole 
matter is now put in question by certain newer types 
of music, in which the previously accepted laws of 
harmony are violated. 

There are individual differences in the appreciation 
of harmony. The ability to appreciate the difference 
between harmony and disharmony requires higher 
development than that required to recognize melody. 
Children differ considerably in their ability in this 
matter, and some are capable of a higher development 
than others. Harmony is, of course, involved in part 
singing, and it is necessary that when children engage 
in this phase of music they should be able to appreciate 
the simpler phases of harmony. It will probably, how- 



MUSIC 111 

ever, never be necessary to go into the explanation of 
the matter in any detail with them, and so we may 
leave it without further discussion. 

Tone quality 

Another refinement which is involved when the 
training in singing is carried beyond the mere ability 
to strike the correct notes in singing melodies, or in 
singing parts in simple pieces, is called " tone produc- 
tion." This involves not merely the ability to sing a 
certain note, but also the ability to produce it in such 
a way that the quality of the voice is pleasing. A tone 
possesses pleasing quality when it is rich and smooth 
rather than thin or rough. The tone quality of a voice 
or an instrument is called the " timbre " of the tone. 
This is involved in the appreciation of the higher or 
more developed phases of music, and it is necessary 
that the child gain an appreciation of it and the ability 
to produce good tone if he is given specialized training 
which either looks toward professional equipment or 
the higher degrees of amateur development. 

While there is not time or opportunity to give much 
individual attention to tone quality in the singing of 
children in the school, considerable improvement can 
be brought about by calling attention of the group as 
a whole to the quality of their voices and by setting 
up standards for imitation. Something may also be 
done in this direction indirectly by requiring the chil- 
dren to maintain good bodily posture. 



112 PSYCHOLOGY OF COMMON BRANCHES 

Individual and age differences 

Individual differences in musical capacity should be 
taken account of in selecting children for training. As 
has been incidentally mentioned, there are large indi- 
vidual differences in children's ability in music. An 
attempt has been made to measure these individual 
differences, and to determine their significance for the 
child's ability to profit by training. C. E. Seashore has 
measured the ability of children to distinguish between 
tones of different pitch and has laid down certain rules 
as to the amount of training which children should 
receive who have different degrees of discrimination. 
Seashore has the following to say on this point :^ — 

The capacity for the appreciation of music is partially 
inborn and partially the result of training. Thus, in judging 
the quality of an instrument or voice, the expert hears and 
observes differences and peculiarities that entirely escape 
the untrained ear; and all differences in the so-called quality 
and timbre of tone are reducible to pitch. But such hearing 
represents a complex process of interpretation, which can be 
mastered only after extensive training. The mere detection 
of pitch difference is, on the other hand, a simple process 
requiring only the slightest amount of training. 

With reference to the bearing of the differences of 
pitch discrimination upon the amount of training 
which the child is capable of receiving, the author has 
the following to say : — 

Suppose we find four children of equal age, advancement, 
and general ability sitting together, and one has a threshold, 

* Psychological Monographs, vol. 13, no. 1 (December, 1910), p. 54. 



MUSIC 113 

for pitch discrimination, of h vd., another 3 vd., another 12 
vd., and another 25 vd. [The symbol vd. means the number 
of vibrations which are produced in a second.] They are to 
have singing lessons. How can we group them properly for 
this period? Nine years ago the author proposed the follow- 
ing classification as a tentative measure [Educational Review, 
June, 1901]: — 

Below 3 vd. . . . May become a musician. 

8-8 vd. . . . Should have a plain musical education. (Singing in 

school may be obligatory.) 
9-17 vd. . . . Should have a plain musical education only if special 

inclination for some kind of music is shown. (Singing in school 

should be optional.) 
18 vd. and above. . . . Should have nothing to do with music. 

The significance of these figures may be grasped by 
the fact that 16 vd. represent one half of the difference 
between middle C and D, the next note above it, or 
about one half step in the scale. 

Results of tests should be applied with discrimina- 
tion. These should be taken as tentative standards, 
and should be interpreted as indicating the degrees of 
ability below which children should not be forced to 
undergo training, rather than as rigid limits marking 
off children who are not to be given training even if 
they are willing or desirous of receiving it. In some 
cases, as in that of a teacher, it is desirable to make an 
especial effort to develop some ability in music even 
though the native endowment in this direction is 
limited. 

Instruction may begin early. With reference to the 
changes in age in discrimination. Seashore has the 
following to say : " In a bright child with a good ear. 



114 PSYCHOLOGY OF COMMON BRANCHES 

the physiological limit can be established for all prac- 
tical purposes as early as the age of five." This means 
that the child can very early distinguish as clearly 
between the different degrees of pitch as can the adult. 
It does not mean, however, that the young child is as 
capable of carrying tunes, or of appreciating the more 
complex features, such as harmony and the composi- 
tion of a piece. These abilities depend not merely on 
the ability to distinguish between tones, but also on 
the ability to carry in mind the relationship of a large 
number of tones to one another, and this ability is 
only of gradual development. The significance of 
Seashore's statement is that the child's musical devel- 
opment may begin at an early age. The development 
of the higher forms must be gradual. 

REFERENCES 

1. C. H. Congdon: The Congdon Music Readers. Chicago. 

2. C. H. Farnsworth: Music in Education. Cyclopedia of Educa- 
tion. Macmillan (1913), vol. 4. 

3. C. E. Seashore: The Measurement of Pitch Discrimination. 
Psychological Monographs (1910), vol. 13, no. 1, p. 64. 



CHAPTER VI 

SPELLING: FIXING OF ASSOCIATIONS 

Learning to spell is a form of memorizing. Memory 
is the means by which those experiences which we have 
had in the past are reproduced in our present experi- 
ence. The particular kind of memory which we call 
"memorizing" consists in reproducing certain defi- 
nite associations which have been formed in the past. 
Memorizing, then, consists in so making associations 
between ideas, or between words which represent 
ideas, that these words or ideas may be recalled in 
the same order in which they were originally formed. 
Spelling may be regarded as exactly the same sort of 
learning. In the case of spelling, the associations which 
are formed are between the successive letters of a 
word, and between the word thus spelled and the 
meaning. This might very properly be called memo- 
rizing, and is one form of memorizing, though the 
term is usually used to designate the formation of as- 
sociations between words rather than between the let- 
ters of a word. 

Accurate spelling is demanded chiefly in writing. 
The problem of learning to spell is one which arises in 
connection both with reading and with writing, but it 
would not be an acute problem if the child never had 



116 PSYCHOLOGY OF COMMON BRANCHES 

to write. He would be able to recognize words with 
suflBcient precision if he did not know their exact 
spelling. Only in certain cases of the close similarity 
of words would any difficulty arise. When it becomes 
necessary to write words, the problem of how to spell 
them becomes important. The child might express his 
meaning fairly intelligibly without learning to spell 
accurately, and until recent times even educated peo- 
ple expressed their meaning through writing in a satis- 
factory way without spelling with any high degree of 
uniformity. The extreme care which is now taken to 
spell a word in a certain conventional way is a rela- 
tively recent development. Formerly people did not 
even spell their names consistently. The school is 
compelled to take the situation as it is, and to recog- 
nize that a person who does not spell words in the 
conventional way is regarded as uneducated by other 
persons, and that such a one is likely to meet with 
difficulty in his business, professional, or social life. 

The associations in spelling 

The ability to spell may be based on associations 
between movements or between elements of percep- 
tion. While the problem of spelling first becomes acute 
as a result of the need of writing, it nevertheless is 
closely related to the problem of learning to read. The 
reason for this is seen when we examine more closely 
into some of the associations which lie at the bottom 
of the ability to spell. Association must always be 



SPELLING 117 

between certain ideas or experiences, and one type of 
experiences which may be associated consist of motor 
activities. In the case of spelhng these activities may 
be the writing of certain letters, and some persons can 
spell the more difficult words only when they write, or 
at least when they imagine themselves to be writing. 
We call this type of association a motor association 
because it consists of connections between movements. 
Or the association may be between movements which 
are made in the pronunciation of the letters of a word. 
This was the common method of spelling in the earlier 
days of spelling instruction. At the present time, when 
the letters are not so much emphasized in learning to 
read, this is not so common. There may be an associa- 
tion, also, not between these forms of movements but 
between ideas or percepts, based upon the perception 
of the successive letters. Some persons can spell most 
readily when they see a word or think of the way the 
letters of the word look. It is with this type of asso- 
ciation that reading has most to do. The impression 
which is made through carefully scrutinizing the word 
as it is read will then be of help in forming the asso- 
ciation between the letters. A fourth type of associa- 
tion, which is used by many in assisting them to spell 
words, is between the letters as they are heard. One 
may either pronounce the letters himself and hear them 
as he pronounces them, or he may hear them pro- 
nounced by another. This is of the same sort as the 
association between the letters as seen, since it is an 



118 PSYCHOLOGY OF COMMON BRANCHES 

association between the objects perceived rather than 
between movements. This form of association does 
not arise in connection with reading, but only in con- 
nection with special training in spelling. 

Spelling instruction should be closely related to 
reading and writing. The fact that a necessity for 
spelling arises in connection with reading and espe- 
cially with writing, makes it necessary, if spelling is to 
be taught in such a way as to have the most meaning 
for the child, that it shall be closely connected with 
reading and writing. This does not mean, as we shall 
see in a later section, that there need not be special 
drill given to spelling; but it means that the words 
which are given in the spelling drill should be those 
which the child uses also in his reading and writing. 
It means that, although it is necessary that the child 
give special attention to the spelling of words, the 
words to which he gives special attention should not 
be out of relation to his experience and meaningless 
to him, but they should be related to the rest of his 
thinking and of his school work. In choosing the 
words which the child is to learn to spell, we must take 
into account those words which he shall have use for 
after he leaves school. Investigations have been con- 
ducted to determine what these words are. When 
these have been found, it is not sufficient merely to 
introduce them into the spelling lesson, but they must 
also appear in the other work of the child, in his com- 
position, in his reading, and so on. 



SPELLING 119 

Why may not the child spell entirely by sound? It 
has been said that learning to spell consists in making 
connections between the acts of writing the letters of 
a word, or speaking the letters, or in making associa- 
tions between the letters as they appear on the page, 
or as they sound when spoken. The question may be 
asked why it is necessary to make these associations. 
Theoretically, as we saw in the chapter on reading, 
the letters of a word represent the sound of the spoken 
word. If this is the case, why, then, may not the child 
merely form once for all the association between a 
sound and its corresponding letter, and thus be able to 
spell any word which he can pronounce? 

Partly because pronunciation varies. There are 
several reasons why this is not sufficient. One reason 
is that the variation in the pronunciation of words 
makes it impossible to be always sure, from its pro- 
nunciation, how a word is spelled. An illustration of 
this fact is given in a book by Owen Wister in which he 
ridicules spelling reform. According to the story, a 
number of enthusiasts for spelling reform met in a 
convention, and attempted to agree how certain words 
should be spelled so that the spelling should conform 
to the pronunciation. One Southern delegate started 
a riot by insisting that courthouse should be spelled 
c-o-a-t-h-o-u-s-e, this being the way in which he pro- 
nounced the word. 

Partly because the same letter often represents a 
variety of sounds. It was noticed in the chapter on 



120 PSYCHOLOGY OF COMMON BRANCHES 

reading that the alphabet which is used in written Eng- 
lish, in common with most of the European tongues, 
has been inherited from the Greeks and Phoenicians 
through the Romans, and that it does not completely 
fit the English language. The same letter often repre- 
sents a variety of sounds. Consider the sound of a in 
bay, bat, ball, bar, ask, autumn, and ribald; of the s in 
sit and business, of the c in cat and receive. Such vari- 
ations as these make it impossible to infer from the 
spelling of a word how it shall be pronounced. 

Chiefly because the same sounds are often repre- 
sented by a variety of letters. The chief reason, how- 
ever, why the spelling of English words cannot be 
learned merely by the connection of sounds with let- 
ters is that the language is not spelled as phonetically 
as it might be. We do not spell the words so as to 
correspond as closely to pronunciation as we might 
even with our imperfect alphabet, and with the vari- 
ety of dialects and modes of pronunciation which 
exist. Various spelling-reform associations have made 
us familiar with the great variety of cases in which the 
same sound is represented in several ways or in which 
the same spelling represents a variety of sounds. The 
following examples may be taken at random. Con- 
sider the different ways in which the sound of long o 
is represented in the following words: so; sew; row; 
though; bureau. So long as our spelling remains in its 
present unphonetic condition, and we have no means 
of knowing how long it may so remain, there is no 



SPELLING 121 

possibility of a child's learning how to spell many of 
the words of our language from their sound. It be- 
comes necessary, then, for him to learn merely by 
forming arbitrary associations between the letters. 

Methods of learning to spell 

So far as possible the child should learn to spell 
from sound. Before going on to a consideration of the 
way in which these arbitrary associations are formed, 
we should keep clearly in mind the fact that in the 
case of those words which can be spelled from their 
sound, the child should learn to spell them through 
connecting the sound with the spelling. The principle 
here is the same one which is found to hold in the 
case of memorizing. It is found that the material 
which is to be memorized should be given a meaning, 
as far as may be, and that rote memorizing should be 
reduced to as small an amount as possible. Similarly, 
we may say that so far as the child can get a clue to 
the spelling of the word from its sound he should do so. 
Furthermore, although there is a variety of ways in 
which the same sound may be represented, yet the 
number of ways is not so large but that the child can 
learn what they are. The child's problem in spelling 
a word which is not phonetically spelled is not to learn 
a purely arbitrary spelling for it, but to learn which of 
several ways of representing that sound is the one 
which is used in this particular word. Spelling is not 
a purely arbitrary affair, and in the case of a great 



122 PSYCHOLOGY OF COMMON BRANCHES 

many words the spelling can be deduced from the pro- 
nunciation. Because the correspondence between the 
sound and the spelling is not complete is no reason for 
failing to make the most of the degree of correspond- 
ence which does exist. 

All available helps from related words, rules, or 
principles should be used to make spelling rational. 
We may say, as a general principle, that wherever the 
spelling of a word can be related to some inclusive rule 
or fact, or may be connected with the spelling of 
analogous words, this should be done. Such relation- 
ships may be found not merely between the sound and 
spelling, but also between the spelling of different 
words which have similar meanings. For example, 
the word laboratory presents a difficulty particularly 
in the syllable which is not accented — the second 
syllable. The fact that o is used here may be connected 
with the word labor. When the child once sees this 
connection, he will easily remember how the longer 
word is spelled. Even more or less arbitrary rules, if 
they serve to bring the spelling of a word under a prin- 
ciple and make of it not merely an arbitrary affair, 
will be useful, such as the familiar rule regarding the 
order of i and e in receive, believe, weigh, etc. 

To fix the arbitrary association the incidental and 
the drill method may be contrasted. After we have 
done all we can to find a connection between the spell- 
ing of a word and its pronunciation or to establish 
other meaningful associations, there remain a certain 



SPELLING 123 

number of purely arbitrary associations which have 
to be made. There is no royal road to spelling. In 
the formation of these associations, which are left over 
after we have exhausted all the logical associations 
possible, there are two general methods of procedure. 
The educational opinion and practice have been di- 
vided upon which of these two methods is the more 
effective and economical. The first method consists in 
allowing the child to learn to spell words merely as 
they happen to come up in the course of his reading or 
of his writing. Some special attention may be given 
to the words as they appear, either in order to antici- 
pate and prevent a child's spelling a word wrong, or 
in order to correct a wrong spelling after he has made 
it; but no attempt is made to give the child a drill in 
the spelling of words in a separate period, or to select 
series or lists of words upon which repeated drill is 
to be given. This is the incidental method. The drill 
method, which is opposed to the incidental method, 
includes the characteristics which have been described 
as being neglected by that method. It takes its name 
from the fact that it applies the principles which have 
been found through psychological investigation to 
produce in the most economical and effective manner 
the associations which are desired to be formed. 

The investigations of Rice and Comman give sup- 
port to the incidental method. Before attempting to 
present more minutely the advantages and disadvan- 
tages of these two methods, we may sketch very 



124 PSYCHOLOGY OF COMMON BRANCHES 

briefly the experiments which have been performed 
in order to compare the efficiency of the two methods 
in actual practice. In the late nineties, J. M. Rice 
startled the educational world by showing, through a 
survey of the results of spelling from a large number of 
cities, that a great deal of the time spent in spelling 
exercises was wasted. This was inferred from the fact 
that many cities in which a smaller amount of time 
was spent secured as good results as did those in which 
a much longer time was taken for spelling. This inves- 
tigation was followed up by another by Cornman, in 
which the experiment was made of entirely eliminating 
the spelhng period from three Philadelphia schools, 
and comparing the result of the incidental method 
used in these schools with the results of the spelling 
drill as used in the remainder. In the incidental 
method, as used in these three schools, considerable 
attention was given to spelling by calling the child's 
attention particularly to the difficult words which he 
was likely to misspell, and by collecting the mistakes 
which he made in his written work. This experiment 
showed that the three schools which used the inci- 
dental method secured as good results as did the others 
which employed the ordinary drill. 

Wallin's investigation turned the scale in favor of 
the drill method. These investigations seemed to 
settle the question in favor of the incidental method. 
There were, however, several weaknesses in the reason- 
ing leading to such a conclusion, and these have been 



SPELLING 125 

shown to be fatal to it in a more recent investigation 
by J. E. W. Wallin, at Cleveland. The Cleveland 
schools had for years used a carefully worked-out form 
of spelling drill under the direction of Assistant Super- 
intendent Warren E. Hicks. Wallin found that as a 
result of this drill a degree of efficiency was reached 
by the children of the Cleveland schools which far 
exceeded that obtained by either the drill group or the 
incidental group of the Philadelphia schools. 

The incidental method is superior only to a poor drill 
method. The results found by Wallin demonstrate 
that the superiority in economy of the incidental 
method, which was used in the three schools in Corn- 
man's investigation, was due to the fact that the drill 
method which was used in the other schools was not as 
efficient as it might have been. On the other hand, the 
incidental method in the three experimental schools 
was probably raised to its highest point of efficiency. 
The average percentage of correctly spelled words in 
the city was about seventy, with two or three per cent 
advantage in favor of the schools which used drill. 
Wallin, on the other hand, found a percentage of cor- 
rectly spelled words, with words of the same character, 
of about ninety-four. This clearly indicates that if the 
drill method is correctly applied, it may give results 
more than twenty per cent better than those obtained 
by the incidental method. 



126 PSYCHOLOGY OF COMMON BRANCHES 

The principles of the drill method 

We turn now to a consideration of the principles of 
drill which are necessary in order that the method may 
be most effective. These principles may be derived from 
the principles of habit formation in general, which is of 
the same character as drill, and therefore are not to be 
thought of as bearing solely upon the teaching of spelling. 

The first principle of spelling drill is sufficient repe- 
tition. As we saw in the chapter on handwriting, the 
cardinal principle of the formation of arbitrary asso- 
ciations is repetition. If we make an association once, 
or several times, but not a sufficient number of times 
so that it is fairly well fixed, we have wasted in a large 
measure the time and effort required to make these 
insufficient repetitions. A number of repetitions spent 
upon a small number of words, sufficient in number to 
make the ability to spell these words permanent, will 
give a definite result. If the same number of repetitions 
are spread over so many words that none of them are 
learned thoroughly, they are largely wasted. This is 
what happens in the case of the incidental method. 
Words are only learned as they occur in the child's 
reading and writing. It is then only a matter of chance 
that the same word occurs with sufficient frequency 
so that the child learns it in the most economical man- 
ner. It is to supply this want that drill is introduced. 

The second principle is adequate attention. The 
next principle of drill has also been met in the consid- 



SPELLING 127 

eration of writing, namely, that repetition made with- 
out giving attention is of Uttle value. This principle is 
sometimes put first and is designated by the term " fo- 
calization." Wlien there is focalization of attention, 
the child has his mind called sharply to the thing he is 
doing. In the case of spelhng, this means that when 
he is learning to spell a word, he is thinking primarily 
of its spelling, and not of its meaning, or of the form 
of the letters as he writes them, or of some other fact 
connected with it. When the child learns to spell 
words incidentally in connection with reading or writ- 
ing, his mind is divided between the spelling and the 
thought which he is getting from the reading, or which 
he is expressing in his writing, and perhaps the form 
of the letters, as has already been suggested. Spelling 
drill, in which the words are studied particularly for 
the sake of knowing how to spell them, calls the child's 
attention to this one fact or aspect of the word, and 
therefore brings about the condition of focalization. 

The third principle is the avoidance of wrong asso- 
ciations. A third principle which has also already been 
met with, and which is particularly important in 
spelling, is the avoidance of wrong associations. The 
drill method attempts to do this in a systematic man- 
ner by anticipating the words which the child is likely 
to misspell and giving him special practice in their 
spelling. An investigation by S. A. Zook^ has shown 

* This investigation is reported in an unpublished master's thesis 
which is on file in the library of the University of Chicago. 



128 PSYCHOLOGY OF COMMON BRANCHES 

that it is desirable, in addition to calling the pupil's 
attention to the word which he is likely to misspell, 
to call his attention also to the particular parts of the 
word where it has been found the children frequently 
make errors. For example, it was found that there 
was frequently confusion as to what part of the word 
the c comes in, in the word scissors. If this is particu- 
larly emphasized in teaching the child the word, many 
errors will be avoided. This, of course, does not mean 
that the wrong spelling is to be suggested, but that 
the correct spelling of the difficult part is to be empha- 
sized. 

Drill may be made effective for spelling in connected 
writing. One of the criticisms which has been made of 
the drill method is that it does not enable the pupils to 
spell the words which they have learned in their spell- 
ing lessons when they write spontaneously, to express 
thought. The results are said not to carry over from 
the spelling lesson to the rest of the pupil's work. This 
defect, however, can readily be avoided, as was proved 
by Wallin's investigation, by giving the pupils prac- 
tice not merely in spelling the words in a column test, 
but also in using the words in sentences, and in con- 
necting the spelling with the meaning. This does not 
violate the principle of focalization, since the spelling 
is the chief subject of consideration. 

Drill need not be uninteresting. Another criticism 
which has been made is that the " spelling-grind " is 
dull and uninteresting, and is deadening to the spon- 



SPELLING 129 

taneity of the pupils. If the drill is properly conducted, 
this criticism does not hold, and the belief that drill is 
uninteresting to the child rests upon a false interpre- 
tation of those things which give him pleasure. The 
child is certainly interested in perfecting his ability 
in various forms of skill and spontaneously practices 
doing many things which involve a large amount of 
repetition and arduous practice. If the work is suited 
to his capacity, and if he can be shown the results, and, 
when necessary, if some external stimulus is given such 
as is furnished by a contest between different rooms or 
between different schools, as was done in Cleveland, 
there is no difficulty in making such a drill of great 
interest to the child. As has been suggested in previ- 
ous chapters, it is desirable not merely to compare the 
child's record with that of others, but also to give him 
some record of his own progress from time to time. 
Through this means it will be possible for him to see 
the results of his efforts, even though he stands toward 
the bottom of the class on account of deficient native 
ability in this particular Une of work. 

The best method of presentation has been studied. 
A good deal of experimentation has been carried on to 
determine what is the best avenue of presentation of 
words and of letters in order that they may be learned 
most economically; and also to determine whether 
persons differ in the avenue of approach which is best 
suited to their individual needs. In attempting to 
answer the first question, classes have been taught by 



130 PSYCHOLOGY OF COMMON BRANCHES 

presenting the words to them through vision, that is, 
by writing on the board, and the results have been 
compared with the results from other classes to whom 
the spelling of the words was given orally; and from 
others who have seen the words written and have also 
pronounced them; and others who have seen the words 
and also have written them, etc. 

Writing is the most effective single method, but a 
variety should be used. In general it has been shown 
that writing the words and seeing them written is the 
most effective form of presentation for all pupils taken 
together. Hearing the letters of the words pronounced 
and pronouncing them, which is the old spelling-con- 
test method, is not so effective. This is probably due 
to the fact that the pronunciation of the letters is not 
closely connected with the sound of the word, and is, 
of course, not so closely connected with the way in 
which the words are spelled in actual use, which is the 
process of writing itself. In general, however, to use a 
variety of methods of presentation is more effective 
than to use one alone, and since there is no reason why 
one needs to be chosen alone, the safe course is to 
present the words to the child by writing, by having 
him write them and pronounce them slowly, and pos- 
sibly by having him say the letters as he writes them. 

A variety of methods takes account of individual 
differences. Another reason why a variety of modes of 
presentation is desirable is that there is possibly suffi- 
cient difference in the type of minds of different pupils 



SPELLING 131 

to make it easier for some to learn through hearing and 
pronunciation than through seeing and writing. The 
differences among pupils in this respect have probably 
been exaggerated, and we do not know with certainty 
to what degree they exist. It is probable that there 
are only a few who represent any extreme type. How- 
ever this may be, there is no harm in presenting words 
in a variety of ways, and if there are pupils who repre- 
sent extreme types, this will be to their advantage. 

Summary. We have attempted to bring out the 
more general psychological principles which are in- 
volved in spelling, and which may be illustrated in 
spelling. In particular, spelling illustrates the drill 
method, and the principles which have been found to 
have a place in spelling are also appropriate wherever 
we are concerned with the formation of more or less 
arbitrary associations, and where we are dealing with 
learning in which there is a gradual progress instead of a 
solution of the problem by means of the understanding. 

REFERENCES 

1. O. P. Comman: Spelling in the Elementary School. Ginn & O). 
1902. 

2. L. P. Ayers: A Measuring Scale for Ability in Spelling. Russell 
Sage Foundation. 1915. 

3. W. F. Jones: Concrete Investigation of the Material of English 
Spelling, etc. University of South Dakota Bulletin. 1913. 

4. J. M. Rice: "The Futility of the Spelling Grind." The Forum 
(1897), pp. 163 and 409. 

6. 3. ^.VJallin: Spelling Efficiency, etc. Warwick and York. 1911. 
6. H. Suzzallo: The Teaching of Spelling. Houghton Mifflin 
Company. 1913. 



CHAPTER VII 

HISTORY: EXTENSION OF EXPERIENCE THROUGH 
IMAGINATION 

General account of imagination 

Learning in history and geography depend upon the 
imagination. Although the same mental processes are 
used in various subjects, certain of them seem to be 
more particularly involved in some of the school sub- 
jects than in others. If we compare the study of the 
two subjects which are about to be considered, history 
and geography, with some of the more elementary 
subjects, such as reading and writing, we find that they 
are distinguished by the fact that the child is intro- 
duced by them beyond his immediate experience. 
Reading and writing as they are used carry the child's 
mind beyond his immediate experience; but in learning 
to read and write the child is dealing primarily with 
material which is presented in perception. In history 
and geography, on the other hand, he is required to 
live through experiences which are remote in time 
from his own life, or which are distant from him in 
place. In history he learns about the lives of people 
in the past, and in geography, he learns about places 
and people who exist on other parts of the earth than 
that in which his home is situated. The mental process 



HISTORY 133 

by which he is able thus to carry in mind the thought 
of distant or remote events, persons, and places, we 
call imagination.^ 

Through imagination present institutions can be 
explained by reference to their history. The school, 
for example, has certain peculiar characteristics. The 
division of the school period into eight years for the 
elementary school, four years for the high school, and 
four years for the college, has a definite historical 
background. The methods of study which are pur- 
sued, the subjects which are included in the curricu- 
lum, and a variety of other matters, are to be explained 
by reference to more or less remote past events. 

Imagination connects our immediate life with events 
taking place in distant parts of the earth. For the 
explanation of many of the events which we observe 
to be going on about us, we must be able to create in 
our imagination persons and things which exist in the 
present time, but in remote places on the earth. As 
this is being written, much of the conduct of residents 
in the United States is governed by the war which is 
being waged in Europe. We are continually creating 
in imagination the scenes of the European conflict and 
considering its bearing on our lives. The world has 

^ Imagination is the mental process by which experience is ex- 
tended beyond the immediately present surroundings. This is done 
in its simplest form in memory. But imagination also extends ex- 
perience much more broadly so as to bring within the scope of 
our thought objects or events which have never been experienced 
by the individual in the form in which they exist in his thought. 



134 PSYCHOLOGY OF COMMON BRANCHES 

come to be so much of a unit through means of trans- 
portation and communication that the use of geogra- 
phy is an everyday affair. 

Imagination which may be present in memory pre- 
pares for freer imagination. A form of imagination 
exists in memory. When we picture to ourselves the 
face of a person whom we know or recall the sound of 
his voice or the pressure of his hand-clasp, we make 
use of a memory image. The first step in the ability 
to think over or to live over in our minds that which we 
have never experienced consists in thus living over our 
own past experience. In this way we first free our- 
selves from the immediate present. In this the human 
being is rather sharply distinguished from the animal. 
So far as we know, the animal is pretty closely bound 
to the sensations or perceptions which he receives 
through stimulation by objects which affect his sense 
organs. We have no evidence that the animal thinks 
clearly of experiences it has had in the past, although 
its past experiences affect its responses, through giving 
objects various kinds of present meaning. 

Sensory experiences may be revived in imagination. 
The human being, as has been said, may revive in his 
experience various kinds of previous experiences. The 
simplest of these are the sensations or simple percep- 
tions. We can call to mind the appearance of the house 
which we saw hours or days or years before. We can 
call to mind, more or less clearly, the sound of the 
voice of persons whom we have known, or the sound of 



HISTORY 135 

music which we have heard. The sensations of sight 
and hearing are the ones which can be most clearly 
reproduced in our imagination, but to some degree we 
can recall the experience of touch and possibly of 
movement, smell, taste, and temperature. 

Images of words are prominent in thinking. There 
is a particular form of imagination which deserves 
special mention. We may recall to the mind not 
merely the appearance of physical objects or of the 
experiences which we get from contact with them, but 
we may also call to mind the sound or the pronuncia- 
tion of words. Words may be represented to us through 
the sound of some particular person's voice or through 
their appearance in writing or in print, or through the 
movement sensations we get in speaking. The partic- 
ular form of the image does not matter. The essential 
fact is that ideas are represented by images of words. 
Many ideas are of such a nature that we cannot think 
of them most clearly by recalling any sort of object, 
but rather by recalling statements in terms of language. 
Take the law of gravitation. The word itself does not 
refer to a thing which we have seen or heard or felt, 
but to an idea, and the recall of the idea is through the 
recall of the word. Or, if we go further and represent 
to our mind the law of gravitation, — that bodies are 
attracted to one another according to the product of 
their mass and inversely according to the square of 
the distance, — it is clear that the words by which the 
idea is expressed are the chief embodiment of the idea. 



136 PSYCHOLOGY OF COMMON BRANCHES 

Take another case. We express the idea of relationship 
of a person to his country by the word " patriotism "; 
but although patriotism may have certain symbols, 
such as the flag, or the ruler of the country, and so on, 
these symbols do not stand for the idea with the same 
degree of completeness as does the word. Very much 
of our thinking, then, is done in words by saying over 
words internally, or in the imagination. Even our 
thinking in regard to concrete objects is accompanied 
by the presence of images of words in our minds. We 
may then distinguish between concrete imagination 
which has to do with objects, and verbal imagination, 
which has to do with words. 

The importance of words in thinking must not be 
overlooked. This fact that verbal imagination is an 
essential means to all our higher and abstract thinking 
should prevent us from misinterpreting the objections 
to verbahsm in teaching or learning. There is a danger 
that the child shall learn to repeat words in parrot-like 
fashion without an understanding of their meaning. 
This is worse than useless. But to set words and their 
use over against thinking, and to imply that we must 
get rid of words in order that we may think, would be 
like getting rid of our feet as a preliminary to walking. 
We must be sure that the child has the experiences 
which give a meaning to words so that he shall not 
merely put words together into phrases and sentences; 
but we must realize that one of the important results 
of education is just this acquirement of meaning by 



HISTORY 137 

words, so that they can be interpreted and used intelli- 
gently. As the child grows older, we find that he learns 
to use more and more verbal imagination, as distin- 
guished from concrete imagination. While the older 
person thinks somewhat in the images of things, yet 
they tend to become less prominent, and he represents 
his thoughts more largely in words. 

There are wide differences in imagery among differ- 
ent persons. Not only are there these differences be- 
tween persons of different ages, but there are also 
marked differences between persons of the same age in 
the definiteness and clearness of their images in general 
and in the preference which they give to images of 
different kinds. Some persons are able to recall very 
clearly such an object as the breakfast table, as was 
found in an investigation by Galton. Others can 
obtain only a very dim image of the articles on the 
breakfast table. Some can recall more clearly things 
which they have seen, others things which they have 
heard, and others even the movements which they 
have performed. 

Methods of teaching should be adapted in some 
measure to these differences. We must to some extent 
take account of these differences, although not to so 
great an extent as has sometimes been thought. The 
way that these facts may be applied was mentioned in 
the discussion of spelling. It is difficult, however, to be 
always sure to what type a person belongs. He is not 
able to tell us himself, unless he is a psychologist, and 



138 PSYCHOLOGY OF COMMON BRANCHES 

there are no simple tests by which we may determine 
the matter. We may apply these facts in two ways; 
first, by so arranging the work that it will appeal to a 
variety of forms of imagination in the children, and 
second, by allowing a child to do a thing in the way in 
which he seems to succeed the best. This does not 
mean that he should be allowed to choose the kind of 
work that he wishes, but rather that he should be 
allowed to adopt the manner of doing the work which 
seems to suit him best. 

Free imagination begins by the modification of 
memory. We turn now to a description of the different 
grades of imagination and of the ways in which the 
different kinds are used in the study of history. The 
simpler type of imagination, as has been remarked, is 
that in which we live over the experiences which we 
ourselves have had in the past. By this means we 
break away from the present. A person may Uve over 
the events of the previous day, or a day in the past 
month, or the past year. When he does this, he soon 
begins to do more than merely to live over his past 
life. He begins to dwell upon certain phases of his 
experiences more than others, and it has been discov- 
ered that the more pleasant experiences tend to be 
retained longer than the unpleasant ones. Further- 
more, he begins to change the character of his experi- 
ences somewhat. Part of this is due to reading into 
the past things which have happened since. Part of it 
is due to putting together things which were not to- 



HISTORY 139 

gether in our past experience. So in a variety of ways 
we take liberties with our past life, and modify it, 
either because of the frailty of our memory, or because 
of a tendency in our nature to dwell upon certain 
experiences rather than upon others. 

The next step is to construct objects in imagination 
different from those which have been met in actual 
life. This modification paves the way for an entirely 
different kind of imagination, or rather one which may 
depart so widely from the first stage of the merely 
reproductive imagination that it becomes radically 
different from it. To take our illustration from the 
life of a child, a child may first recall to mind experi- 
ences he has had with an object, as, for example, a 
dog. After he has become somewhat accustomed to 
this procedure, he may follow a story which is told 
him, relating to a dog, by supplying the picture of the 
dog which he knows. He thus uses his past experiences 
to fill out and make concrete events which are being 
related to him. As he acquires wider experience with 
dogs, he is likely to use, not the image of some particu- 
lar dog, to make a story about a dog concrete, but an 
image which differs from particular dogs of his ac- 
quaintance and is constructed for the purpose of the 
story. 

Imagination uses old material, but combines it in 
new ways. This illustrates a general principle regard- 
ing imagination. Imagination does not create any- 
thing absolutely new so far as the material of thought 



140 PSYCHOLOGY OF COMMON BRANCHES 

is concerned, but enables us to rearrange into new 
combinations or into new forms the materials which 
have been furnished to us by our past experience. 
We may create these forms in our imagination as a 
means of following a story or description which is 
made by another person, or we may spontaneously 
create new combinations, as when we try to invent 
a new machine or the plot of an original story. 
When we merely follow the lead of another, the 
process may be called " constructive imagination," 
and when we spontaneously form in our mind events 
or objects which have not been present in our past 
experience, we term the process " creative imagina- 
tion." The form of imagination in which we merely 
live over our past experiences may be termed, in con- 
trast with these, " reproductive imagination." The 
distinction between these three is not always entirely 
sharp, but they may serve to represent types which are 
distinct in their main characteristics.^ 

The great stimulus to the development of imagina- 
tion in the child is language. The use of words by 
other persons is a continual challenge to the child to 
form in his mind ideas which correspond to these 
words. This he does by the recall of his previous 

^ Reproductive imagination is the type which is illustrated in 
memory. Constructive imagination is involved in the study of 
history and geography, in which we form in our minds ideas cor- 
responding to definite requirements which are imposed upon our 
minds from without. Creative imagination is involved in inven- 
tion, or in literary productions. 



HISTORY 141 

experiences, or by anticipating in imagination experi- 
ences which he will have in the future. He hears older 
persons talk about the happenings of the previous day, 
and this causes him to recall them also to his own 
mind. He hears discussed in the family circle the plans 
for the next day or the next week, and this leads him 
to look forward. The conversation of others creates 
a stimulus to the formation in his mind of ideas which 
have not been present at all in his past experience, 
but which may be formed by putting together ele- 
ments out of his previous experience. 

The child's imagination is little hampered by re- 
strictions set by natural law. A child's mind is par- 
ticularly apt in creating with great freedom new com- 
binations in his imagination. He has not had sufficient 
knowledge of the ways in which different things 
may be expected to combine, or of the laws which 
govern their combination, so that he is particularly 
hampered by such conditions. He can put things to- 
gether in his imagination which are impossible for the 
adult, from the fact that the adult is aware of their 
improbability. To the child few things are improbable 
and still fewer are impossible. The myths and fairy 
tales with which he is regaled are appreciated by him 
because the combination of events and of things which 
are related in them does not strike him as absurd. That 
Santa Claus can drive his reindeer through the air, and 
can come down through the chimney, are, to be sure, 
in contradiction of any events which he has experi- 



142 PSYCHOLOGY OF COMMON BRANCHES 

enced; but his sense of law and order is not yet suflS- 
ciently developed to make it difficult for him to believe 
that such things can happen. 

The child cannot guide his imagination according to 
definitely prescribed conditions. While the child's 
imagination seems to be more active than that of the 
adult because of his greater freedom from the restric- 
tions which are imposed by natural law, he is inferior 
to the adult in the kind of imagination which is de- 
manded in history. As we shall see shortly, it is neces- 
sary, in order to understand history, to construct an 
idea of the physical surroundings, manner of life, and 
mental attitudes of persons who are remote from our- 
selves in time and customs. This means that we must 
break away in a measure from the restrictions of our 
accustomed experiences, and also that in constructing 
the new conception we must faithfully follow the pre- 
scriptions which are laid down for us by the historian. 
It is in the ability to follow definite prescriptions so 
as to gain a faithful historical conception that the 
child is deficient. 

Imagination need not be fanciful, but may be based 
on facts. The distinction which was made in the pre- 
ceding paragraph suggests a characteristic of imagina- 
tion which is in danger of being overlooked. We often 
think of imagination as something which is purely 
fanciful, something which is unreal or untrue to our 
experience. The child is particularly adept at this 
type of imagination. The other type which requires 



HISTORY 143 

the construction in our mind, according to certain 
definite principles, of conditions which are different 
from those in which we live, is equally genuine, and is 
one of the most important requirements of scientific 
thinking. The geologists create a different world from 
that which exists at the present time by taking a few 
bones and fossils of plants and building an environ- 
ment about them by the application of the laws and 
principles which we find to be present in the world 
about us. They determine what the conditions of life 
and the appearance of the earth must have been in 
past ages, and are able to draw a picture or to con- 
struct a model which represents in its general features 
what these conditions were. The historian is able to 
do the same thing for the life of people who have 
existed centuries ago. This is the type of imagination 
which is not at all fanciful, but which is determined by 
fixed laws and principles. 

The types of imagination employed in history 
Imagination of concrete objects 

History involves the creation of persons or places in 
the mind's eye. Some kinds of historical appreciation 
involve certain types of imagination, and others in- 
volve others, and what these are we shall have to con- 
sider more particularly. In the first place, we must 
use in history the same type of imagination which we 
use in the appreciation of fiction. When we tell the 



144 PSYCHOLOGY OF COMMON BRANCHES 

child about historical persons, he has to create some 
sort of image of these persons in his mind, in exactly 
the same way as when we tell him about persons who 
only exist in fiction. This type of imagination enables 
the child to appreciate the earlier and simpler forms of 
history, which we may designate the " Once-upon-a- 
time " kind. It is not necessary that the child should 
locate the persons in definite time, or in definite order 
with reference to one another. By means of this kind 
of historical narrative he becomes acquainted with 
some of the important personages with whom he will 
later deal in a more systematic way. The only differ- 
ence between this kind of history and fiction is that in 
the one case the characters have actually existed, 
whereas in the other they have not. 

Familiarity with the biography of historical persons 
prepares for the appreciation of their historical rela- 
tions. As has been said, it is worth while to use his- 
torical personages in the stories which are told the 
child, because it prepares him to weave these person- 
alities into the web of historical account which will 
later be related to him. It will then be easier for him to 
follow the later accounts since the elements are familiar 
to him. This type of history is suitable to the child 
from the time when he can first appreciate it, that is, 
from about the third year, until he is about nine or ten 
years of age. 



HISTORY 145 

Temporal imagination 

Complete understanding of history includes placing 
events in a time order. In order that the child may 
progress beyond this stage, it is necessary that he be 
able to place the historical personages in past time, 
and in definite order in time with reference to one 
another. This rests upon the development of another 
type of imagination, which we shall call " temporal 
imagination." The stories relating to primitive life of 
mankind, which are used in the primary grades, do 
not give the child a true historical notion of the way 
in which civilization has developed from primitive life 
down to the life which we find about us at the present 
time. They prepare him for a later appreciation of 
such development, much as do biographies. That 
they cannot give the child a notion based on the con- 
ception of the succession of different stages of develop- 
ment in time may be seen from the fact that, according 
to the Binet Scale for testing intelligence, the average 
child does not until his sixth year appreciate the differ- 
ence between morning and afternoon. It is to be said 
that this scale is too easy for the average American 
child, but it is such a far call from the simple apprecia- 
tion of the difference between morning and afternoon 
to the understanding of development which has ex- 
tended through thousands of years, that it is incon- 
ceivable that the primary child gets much more than 
a series of pictures from tales of primitive hfe. That 



146 PSYCHOLOGY OF COMMON BRANCHES 

these tales are suitable for the child from other points 
of view is, of course, not called into question. 

The idea of long stretches of time is related to the 
perceptions of short intervals. The child gets his idea 
of the passage of time and of events, as being more or 
less distant in the past or future, as an outgrowth from 
his immediate experience with time. He first must 
learn to distinguish between events which are near at 
hand in the past or the future, and then, after time 
has come to have a meaning for him, he can apply it 
to the arrangement of more widely separated and 
farther distant events. What we call " temporal im- 
agination," or the idea of time, is undoubtedly based 
to some extent on what may be called the " time 
sense," or the immediate perception of the passage of 
short intervals of time. Experiments with adults upon 
the time sense indicate that it is subject to a good deal 
of variability according to the circumstances. If a 
person is anxiously expecting some event, such as the 
arrival of a friend, the time will seem very long. If, on 
the other hand, he is not definitely expecting an event, 
and is engaged in some occupation which absorbs his 
attention, he may greatly underestimate the passage 
of time. The overestimation of the passage of time is 
expressed in the common proverb, " A watched pot 
never boils." 

The child is deficient in time sense. Both experi- 
mentation and ordinary observation indicate that the 
child's time sense is much less accurate than that of 



HISTORY 147 

the adult, and that the variations due to the manner 
in which the mind is occupied are much greater in the 
child than in adults. The child is deficient in the abil- 
ity to imitate rhythm, and grossly misjudges the lapse 
of time. A child becomes very impatient when wait- 
ing for an expected event. On the other hand, if he is 
absorbed, it sometimes appears that he has no sense 
of time. If a child is sent on an errand, and if his atten- 
tion is attracted by some occurrence on the way, he 
does not realize the length of time which he spends 
in stopping to watch the interesting occurrence, and 
arrives home late. 

The recognition of long periods of time depends 
partly on the time sense and partly on the observation 
of external events. The idea of time, or temporal 
imagination, is undoubtedly based to some extent on 
this fundamental time sense. The time which elapses 
l>etween breakfast and the midday meal and between 
this and the evening meal is appreciated vaguely by 
means of the direct experience we have of the passage 
of time. In order that the time idea shall be more defi- 
nite and extend to longer periods, it is necessary that 
we observe other facts and use them to mark off defi- 
nite divisions of time. The way in which the larger 
divisions of time are marked off indicates that we are 
thus dependent upon external events, and not merely 
upon our own appreciation of the passage of time, in 
order that we may get a unit of time and may apply it 
in the estimation of the longer periods. The year, for 



148 PSYCHOLOGY OF COMMON BRANCHES 

example, represents changes in the seasons, the month 
marks the phases of the moon, the day the rising and 
setting of the sun, and so on. The smaller divisions of 
the day, except those between midday and morning or 
evening, are not distinguished sharply unless we have 
watches or clocks which give us the means for marking 
off the hours. The inferiority of the young child in the 
recognition of periods of time, then, depends partly 
upon an undeveloped time sense and partly upon the 
fact that he has not been led to observe the signs which 
mark the divisions of time, and to use them to set in 
order his memories of what has happened in the past 
or his anticipation of events in the future. 

The child learns to distinguish periods of time 
through his everyday experience. As indicated in the 
preceding paragraph, the child first makes the distinc- 
tions which are called to his attention by the practical 
needs of his life. He will distinguish between morning 
and afternoon, when during the forenoon he is prom- 
ised something which is to occur in the afternoon. 
Again, during the afternoon his recollection of the 
forenoon and his discrimination of that period from 
the rest of the day may be stimulated by conversation 
about something which occurred then. The distinc- 
tion between day and night is called sharply to his 
attention both by the fact that the sun goes down in 
the evening and rises in the morning, and also by the 
fact that morning and evening mark important turn- 
ing-points in his experience, in that he goes to bed 



HISTORY 149 

at night and gets up in the morning. Similarly, he is 
led gradually to make the distinction between yester- 
day and to-morrow through recalling the events of 
yesterday or anticipating those of to-morrow. The 
reward or punishment which he may have received for 
acts done previously is one method by which this dis- 
tinction is called to mind; and in a similar way, the 
promise and fulfillment of results of his actions of 
to-day call to his attention the coming of to-morrow. 

Longer periods are recognized in the same way. 
The recognition of larger divisions, such as that of the 
week, is produced in a similar way by the events of his 
life which occur at the end of the weekly period. When 
the child goes to school, his attention is called to the 
fact that Saturday is marked off by the holiday 
which occurs on that day, and that Sunday brings a 
still different manner of life, such as putting on his 
best clothes and going to church or Sunday School. 
The division into still longer periods of time is called 
to his attention by the presence of other holidays or 
vacations, or events which occur in a periodic way. 
His birthday, for example, helps to bring to mind 
vaguely, and later more clearly, the notion of the 
year. 

Number is necessary to the clear idea of long periods 
of time. Any near approach to an exact notion of the 
longer periods of time requires that the child shall not 
only remember and anticipate in a general way, but 
that he shall make definite the duration of time inter- 



150 PSYCHOLOGY OF COMMON BRANCHES 

vals through the use of number. We can, perhaps, get 
an appreciation of an hour or a day merely by the 
direct experience of the passage of time or by the time 
sense; but the appreciation of a month in any definite 
way means that we have a definite number idea of the 
meaning of thirty as a multiple of one day. In the 
case of the longer stretches, such as a year, it is obvi- 
ously impossible to appreciate them merely by the 
direct time sense. We may, therefore, assume that 
the child gets only a very vague and indefinite notion 
of longer time until he has a sufficiently clear idea of 
number to put the time intervals into definite numer- 
ical form. 

The abstract notion of even the longer periods may 
be made somewhat concrete by observing natural 
events. The appreciation of time through the obser- 
vation of such events, as well as by means of the num- 
ber idea, rests upon forms of experience which the 
child gets only gradually and does not attain at an 
early age. All of these forms of analysis of the tem- 
poral imagination indicate that it is a matter of grad- 
ual growth on the part of the child, and make it clear 
that the degree of clearness which is necessary for the 
appreciation of definite historical sequences is not to 
be looked for until the child has been in school for at 
least three or four years. Even then the development 
is not completed, but is only thoroughly started. 

First historical narratives should be simple. These 
conclusions, if well founded, can only lead to the posi- 



HISTORY 151 

tion that the historical narratives which are designed 
for the child must at first be simple and easy to follow. 
In the first place, they must not cover very long periods 
of time. Even the account of the life of a single indi- 
vidual is beyond the grasp of a child at first. Further- 
more, the various series of events must not be com- 
plex. It is easier to follow the life of one individual 
than it is to follow the lives of several individuals who 
are contemporary with one another. It is easier to 
follow the history of one section of a country than the 
parallel histories of all sections. It is easier to follow 
the history of one country than the history of several 
countries which are interwoven in their relationships 
with one another. The difficulty, however, does not 
depend so much upon the breadth or extent of the 
fields covered as upon the minuteness with which the 
train of events within a certain field is followed out. 
The life of one person may be very complicated if the 
relationships of this person to others, and to the events 
of the age in which he lived, are followed out in full 
detail. On the other hand, the history of a country 
may be made very simple by the selection of a few rep- 
resentative events which portray certain phases of its 
development. We may say, then, that the history 
which is designed for a child must be simple, and 
furthermore, that it is easier to simplify the history of 
one country than it is of several related countries. 
Therefore, it is best to begin with the history of a 
single country, and after that has been followed and 



152 PSYCHOLOGY OF COMMON BRANCHES 

the child has got some conception of its development, 
it is time to relate the history of other countries to it. 

Begin with recent history and pass from that to 
remote events. The problem then arises as to which 
country should be treated at the beginning and as to 
the way in which the history of the country which has 
been chosen should be developed. The psychology of 
the development of the idea of time, as it has been 
outlined, throws some light on this problem. We have 
found that the child first recognizes the differences of 
time which are immediately in the past or the future; 
that he begins with his own personal experience and 
reaches out from it before and after. If we follow this 
same process in the early history which the child is 
taught, we should begin with his own country, with 
which he has immediate experience, and should teach 
the child comparatively recent history at first, rather 
than begin with remote past time and work forward. 
We cannot, of course, carry out the principle of begin- 
ning from the present and working backwards, in the 
full and strict sense, as one may reverse a moving- 
picture film; but we may follow the psychological order 
by relating the history of events which are near the 
child and gradually extending them to those which 
are more remote in the past. 

This method connects history with present life. 
When we do this, we make of history something which 
is of immediate connection with the child's present 
experience, and which lends significance to the prob- 



HISTORY 153 

lems which arise in his own life and throws some light 
upon their solution. History may be regarded as an 
account of the origin of those facts and those beings 
which are in existence at the present time. In tracing 
the origin of those facts or beings, we begin with their 
immediate past and then work gradually farther and 
farther toward their more remote antecedents. If we 
begin, in teaching the child, with the remote antece- 
dents of present-day people, or with the remote causes 
of existing physical objects, he loses the connection 
between the present results and the remote past cause. 
He then fails to get the conception of history as having 
a direct and important relationship to his present-day 
affairs. 

History involves spatial imagination. Historical 
events are, of course, not only related in time, but are 
also related to one another in space, since they take 
place at particular localities upon the earth. The 
child is required, therefore, in any complete apprecia- 
tion of history, not only to be able to put the events 
together in a certain time order, but also to create in 
his imagination the geography of these events. This 
form of imagination will be treated particularly in the 
chapter on " Spatial Imagination," or " Geography." 

The historical sense 

The child at first fails to make allowance for the dif- 
ferences between past and present life. When the 
child is first told of persons or places which existed in 



154 PSYCHOLOGY OF COMMON BRANCHES 

the past, he has a strong tendency to think of them as 
like the persons with whom he has been famihar in his 
own experience. He merely transfers in imagination 
those things, those scenes, and those persons which he 
has met in his own life to a previous period, and puts 
them into the story which the history relates, modify- 
ing them as may be necessary to suit the events. In 
his early acquaintance with history, the child does not 
recognize the difference in the physical surroundings, 
or the difference in beliefs and mental attitudes, which 
characterized people of past time in contrast to those 
of our own time. 

The difference in physical surroundings is appreci- 
ated first. The ability to appreciate the difference in 
physical surroundings is the easier one to acquire, and 
the one which the child can acquire in a more or less 
superficial way by the use of pictures and other con- 
crete means of representation. Still, it requires a 
fairly good degree of ability in constructive imagina- 
tion to picture to one's self clearly the houses, the land- 
scapes, and the costumes of the people of past times. 

The appreciation of differences in mental attitudes 
is difficult even for adults. The difficulty of realizing 
to one's self the difference in physical surroundings is 
very much less than that which attaches to the appre- 
ciation of the differences between the mental attitudes 
of persons of past time and those of our own contempo- 
raries. Even our ancestors of one hundred years or 
one hundred and fifty years ago differed from us so 



HISTORY 155 

radically on certain questions that it is difficult for us 
to understand how they could have held some of the 
beliefs that were common. To take an example from 
our own country, a justification of the attitude of the 
colonial settlers toward witchcraft is inconceivable to 
us. It is even becoming difficult for us to understand 
how there could have been any real difference of opin- 
ion on the question of slavery. If an adult finds it 
difficult to project himself into the mental life of a 
past people, even of those who are his immediate 
ancestors, it is an impossibility for the child to do so 
with any degree of completeness. 

The historical sense extends the attitude of toler- 
ance to persons who lived in the past. This type of 
imagination, which has been called the " historical 
sense," is in reality merely an extension of the process 
which the educated adult carries on when he gains a 
proper degree of insight into differing points of view 
of other persons with whom he comes in contact. Vari- 
ous groups of people in the same society differ in their 
attitude on all sorts of questions. A hidebound adher- 
ent to one political party can as little conceive how 
any one can conscientiously uphold the foolish princi- 
ples of the opposing party as can the average person of 
this age conceive how a rational person could have 
believed the things which our ancestors believed. Wliat 
we are considering here is merely the extension to wider 
differences of this same tolerance and understanding. 
This extension must be built upon somewhat more 



156 PSYCHOLOGY OF COMMON BRANCHES 

abstract material. In understanding the attitudes of 
historical persons we have to create for ourselves their 
lives and attitudes on the basis of written records and 
traditions, rather than on the basis of contact and 
conversation with them. We believe that an increase 
in tolerance is being attained by modern civilized 
people, and similarly, the historians tell us that the 
fully developed historical sense is distinctly a feature 
of modern scholarship 

The historical sense has little possibility of develop- 
ment before adolescence. The child can begin at a 
rather early age to gain in the appreciation of the 
difference in physical surroundings of past people, but 
the full development of even this type of historical 
sense is not consummated early. The higher type of 
historical sense, which deals with mental rather than 
with physical facts, is probably very slightly developed 
before adolescence; and then it has only a gradual 
growth. It appears from the recorded observations 
and investigations of children that the ability to appre- 
ciate the motives of others, to understand motives 
which are different from one's own, and to judge of 
one another's conduct by considering motive as well 
as actions, is an attainment which is not reached be- 
fore adolescence. If this is true, it is futile to attempt 
to discuss with the child to any great extent the dif- 
ferences in point of view between ourselves and people 
of the past, and to explain them on the basis of the 
growth of morals or of customs, as can be done with 
the older pupil. 



HISTORY 157 

The grasp of historical development 

Two other forms of mental ability are prominent 
in the appreciation or study of history in its full 
meaning, although they are not, strictly speaking, 
forms of imagination. In order to round out our ac- 
count of the mental processes in the study of history, 
however, we may include a brief discussion of them. 

History attempts to explain events by previous con- 
ditions and events. The jfirst form of history in the 
mind of the child is merely a narrative, that is, a series 
of events occurring in time. These events are related 
to one another, but not in such a way as to make 
prominent the idea that the later events grow out of 
the earlier ones as their cause. The degree to which 
the study of cause and effect can be carried on in his- 
tory is a question on which there is a division of opin- 
ion. Some students of history have attempted to give 
a very minute account of the course of human events 
as illustrating the law of cause and effect. The discov- 
ery and formulation of general laws with reference to 
historical development has been attempted. Although 
one may not agree with the extreme form of this view, 
yet historians do occupy themselves with such ques- 
tions as are being considered at the time of this writing 
with reference to the European war. Not only his- 
torians, but all persons who have any interest in the 
matter, are desirous of knowing what the causes of 
such a tremendous conflict are. Was the war caused 



158 PSYCHOLOGY OF COMMON BRANCHES 

by the machinations of a few individuals, or by the 
ambitions and desire for territorial expansion on the 
part of a war party; or was it caused by the expansion 
of peoples, or their desire to gain for themselves the 
good things of the earth; or was it caused by an inevit- 
able conflict of races; and so on? In order to gain any 
light at all on such questions, we must study events 
which have led up to such a consummation as this, 
and we must give these events an interpretation. As 
in the case of the historical sense, it is probable that 
children gain little appreciation of this phase of his- 
tory until they reach the adolescent period. 

Critical examination of sources 

Another phase of the study of history has not to do 
so much with the understanding of historical facts 
after they have been gathered as with the method by 
which they are gathered and determined upon in the 
first place. Ancient historians discriminated very 
little between tradition, which had no foundation in 
fact, and reliable sources of evidence. We may say 
that what is regarded as the scientific method of ob- 
taining facts is the most prominent characteristic of 
modern historical scholarship. 

The examination of historical sources is an exam- 
ination of witnesses under diflSculties. In order to 
ascertain the reliability of records which purport to be 
historical, it is necessary that the same procedure be 
carried out, in a modified and more difficult form, that 



HISTORY 159 

is taken to find out the truth regarding contemporary 
facts. Courts of law have developed an elaborate 
procedure by which facts in a disputed case may be 
discovered. We know that even in the case of current 
events, it is difficult to be sure what is the truth and 
what is fiction. The examination of witnesses and the 
criticism of their testimony are now being studied in a 
scientific way. We may regard historical records as 
testimony of witnesses to be examined in the same way, 
with the added difficulty that they cannot be cross- 
questioned. The possibility of prejudice or of the dis- 
tortion of evidence because of personal interests are 
matters which have to be considered. When a his- 
torian attempts to determine what are the facts in 
regard to the conduct of a war, for example, he can 
find conflicting evidence in newspaper reports which 
are pubhshed in the different countries. It is his busi- 
ness to decide what the truth is by comparison of the 
different sources of evidence. 

Critical examination of sources is too difficult for 
high-school pupils. It is sometimes the fashion to use 
a good deal of source material in the teaching of his- 
tory to young people. It is questionable, however, 
whether they are able to carry on the very difficult 
and complicated sort of examination of sources which 
is necessary to get anything of value from them. It is 
perfectly possible and altogether desirable to make 
historical accounts concrete and vivid by introducing 
certain forms of source material whieh are agreed upon 



160 PSYCHOLOGY OF COMMON BRANCHES 

as reliable and which do not need to be examined crit- 
ically. But this is a different matter from the examina- 
tion of source material for the purpose of determining 
upon its reliability. It is probably safe to say that 
practically none of this kind of examination of sources 
is suitable for the pupil of high-school age, and that 
little of it can be done to advantage before the later 
years of college work. 

Summary. In summary it may be said that the 
study of history has its chief value and purpose in the 
enrichment of the imagination of the child, by extend- 
ing his experiences into the antecedents of the life in 
which he finds himself. This extension of his experi- 
ence backwards enables him the better to understand 
the life in which he participates, and because he can 
better understand it he can better take his part. As a 
result of the study of historical development he may 
grasp something of the trend of present events. He 
may avoid repeating old errors and may help to carry 
forward the community life in the direction of progress. 

REFERENCES 

1. J. R. Angell: Psychology, chap. 8. Holt, 1910. 

2. H. E. Bourne: The Teaching of History and Ciiics. Longmans, 
1903. 



CHAPTER VIII 

GEOGRAPHY: EXTENSION OF EXPERIENCE THROUGH 
IMAGINATION 

In the introduction to the previous chapter, it was 
shown that our experience may be extended beyond 
the confines of our own immediate surroundings, in 
the imagination of events in past or future time, or of 
those events which are distant in space. It is with this 
latter kind of imagination that we are concerned in 
this chapter. The means by which the location of 
places upon the earth becomes organized in our minds 
is the systematic presentation of the facts which 
constitute geography. It is not necessary to make a 
sharp distinction between geography and the simpler 
forms of astronomy, since we can understand the 
occurrences upon the earth only by understanding its 
relation to the sun, the moon, and the other heavenly 
bodies. 

This treatment does not disparage physical and 
commercial geography, which are important. In con- 
sidering the phase of geography which deals with the 
location of places upon the earth, it is not necessary 
to assume that other forms of geography, which have 
become prominent in the schools in recent times, are 
not to be included in the study of this subject. Physi- 



162 PSYCHOLOGY OF COMMON BRANCHES 

cal geography, as an account of the way in which the 
earth has developed, and of the varieties in physical 
structure of the continents and the other features of 
the earth's surface, is a desirable part of the study, 
since it gives the child a conception of the origin of 
the earth in its present form. Similarly, the study of 
the natural products of various parts of the earth's 
surface, and of the effect of altitude, or of latitude, or 
of other physical conditions upon the life of men and 
upon their occupations, — all of which we include 
under the head of " Commercial Geography," — is 
highly appropriate as a subject to be taught in the 
school. 

The other phases of geography belong to natural 
science. While recognizing the importance of these 
topics, we may still hold to the belief that the funda- 
mental conception which underlies the understanding 
of these other matters is the localization of the dif- 
ferent parts of the earth. This means the ability to 
picture in the mind different localities, their distance 
from each other, and the direction which routes from 
one place to another have with reference to each other. 
Since the other two phases of geography are by nature 
related more closely to natural science than they are 
to location or place geography, we may include them 
in a general way in the consideration of natural science 
and confine ourselves here merely to what we may call 
" spatial imagination," or localization of places upon 
the earth. 



GEOGRAPHY 163 

Growth of spatial imagination or orientation 

The development of spatial imagination is gradual. 
The ability to picture to one's self the location of a 
variety of places on the earth with reference to one's 
own location, and with reference to one another, or the 
more complicated form of imagination by which one 
pictures the relationship of the planets to the sun or to 
one another, and their movements, is subject to devel- 
opment through certain stages, as is temporal imagina- 
tion. The child comes only gradually to the fully 
developed ability in this as in other forms of learning. 

The idea of direction is based on the sense of bodily 
position and movements. As in temporal imagination 
the child first gains the ability to think of events in 
the immediate past or future, so in the case of spatial 
imagination he first becomes able to think of objects 
or places which he does not see, but which are in his 
immediate neighborhood. This ability is the out- 
growth of the localization of sound which the child 
gains when he hears a sound behind him and turns his 
head in its direction. The child learns in the first year 
to do this quite accurately. The later development 
consists in imagining the source of a sound without 
looking around, and then in imagining the location of 
other objects which are behind him, or which are out 
of the range of his vision, without turning around to 
see them. In the earlier case one thinks of a sound 
very much in the terms of the change in bodily position 



164 PSYCHOLOGY OF COMMON BRANCHES 

which one would take in order to turn toward the 
sound. This is one of the fundamental facts which is 
characteristic through all forms of our ability to locate 
direction. We think of the direction of a place with 
reference to our bodily position, and the direction is 
represented in our mind in a large measure in terms 
of the change in bodily position, as in turning the head 
or in pointing, which would bring us into a different 
relation toward the place. 

The localization of directions is gradually extended 
to more distant objects. The development of this 
ability to localize places which are not seen is gradu- 
ally extended. The child learns not merely to place in 
his imagination objects which are in the room or which 
might be seen, but also those which are at a greater 
distance and which cannot be seen from his present 
position. After a few years, at perhaps four or five, 
the child comes to have a fairly definite notion of 
direction of buildings or of streets which are in the 
immediate vicinity of his home, and he can point in 
the general direction of familiar objects which he can- 
not see. 

Orientation with reference to one's self leads to 
orientation of places with reference to one another. 
The whole process of localization we call " orienta- 
tion," ^ and it has become evident that orientation be- 

* Orientation is the localization of objects in imagination either 
with reference to one's self, to one another, or to fixed, standard 
directions. 



GEOGRAPHY 165 

gins with the locahzation of places near one's self, and 
that it has a close connection with one's sense of bodily 
position. Orientation is in the first instance a sense 
of the position of other objects with reference to one's 
self, or the sense of one's own position with reference 
to other objects. This primitive form of orientation, 
which we may call, perhaps, "personal orientation," 
or " variable orientation," is a step in the develop- 
ment of a wider form of orientation .which is more 
fixed in its nature. In this more highly developed form 
the child learns to think of a number of places as hav- 
ing a fixed relationship in space to one another. After 
the child has learned the direction of different build- 
ings and streets with reference to himself when he 
occupies various positions among these places, he 
builds up a notion of their directions and distances 
with reference to one another, which does not depend 
upon his position in the group. He learns to think of a 
street, with the buildings which are located on it, with 
its relationship to other streets. This depends on the 
ability to take a detached view of a region as though 
it were seen from a distance. 

Objects are further oriented by being put into a 
system of fixed directions. This development of a 
more extensive and a fixed orientation usually takes 
place through relating different positions or directions 
with reference to the position of some fixed object or of 
some fixed direction. Whether or not this is always 
the case in the young child, at least it is the means by 



166 PSYCHOLOGY OF COMMON BRANCHES 

which the more compHcated forms of orientation are 
developed. The early mariners used the north star as 
a point from which they reckoned their positions, and 
the directions of places toward which they were sailing, 
and we still use the north and other points of the com- 
pass to enable us to organize the great variety of 
directions and locations which we meet with in our 
different experiences. The use of some such fixed point 
of reference, then, is almost necessary for development 
of any high degree of orientation. Here, again, we find 
that bodily position and bodily movements play a 
large share in the development of orientation. After 
one has determined upon the point of reference with 
which the various places are to be located, he can form 
the ideas of the location of these places by facing the 
standard direction, and then, either actually or in 
imagination, turning toward the different individual 
places. 

The correction of false orientation makes us con- 
scious of the nature of the process. Such a system of 
orientation as has been described is built up so gradu- 
ally, and, in many cases, so early in life, that it is diffi- 
cult to recall the steps through which it has passed, or 
even to realize that the system exists. It is brought 
forcibly to mind, however, in those cases in which we 
form a wrong orientation. If we go to a new town and 
immediately get the directions correct and realize the 
position of the town with reference to north, south, 
east, and west, the whole system of orientation is built 



GEOGRAPHY 167 

up without our being conscious of it. But when we 
have made a mistake and have got these directions 
wrong from the start, we find that the correction of 
the mistake is very difficult. We become conscious of 
the strength of the bonds between the various points 
or directions of the place and the general points of the 
compass when we attempt to change them, in order to 
relate the buildings and streets in detail to a different 
position of the cardinal points. 

False orientation has to be readjusted piecemeal. 
The great confusion which results in such a case of 
mistaken orientation and the process by which it is 
necessary to correct the mistake are instructive as to 
the way in which orientation is built up in the first 
place. We find in such cases that it is not possible to 
correct the mistake we have made once for all, that is, 
merely by recognizing that we have reversed the direc- 
tions of north and south, or have thought of north as 
east; but that it is also necessary to change the direc- 
tion and locations in our mind of every part of the city 
which we have formerly thought of with the wrong 
orientation. It becomes necessary, so to speak, not to 
turn about our idea of the city as a whole, but to re- 
arrange it piecemeal, to readjust every small section, 
with which we have become acquainted, by itself, 
until finally the whole becomes readjusted. 

Orientation is in part built up by relating parts indi- 
vidually to cardinal points. This fact indicates that in 
our first acquaintance with the diflPerent parts of a 



168 PSYCHOLOGY OF COMMON BRANCHES 

place, we adjust each by itself with relation to the 
cardinal points of the compass, and we think of each 
part thereafter, without being fully aware of it, as 
related to these cardinal points. Our idea of a house is 
not merely the idea of its location in a certain part of 
a city, but also of the house as facing east or west or 
north or south. When we have thus become accus- 
tomed to the direction of the facing of the house, we 
have to readjust our ideas with reference to this house 
itself and not merely with reference to the place as a 
whole. At least, while it may not be necessary to 
carry out the process in every detail, it is necessary to 
go into a considerable amount of particular readjust- 
ment in order to correct the original false orientation. 
The child gradually gains a conception of the cardi- 
nal points. Just as an adult, in coming to a new place, 
gradually becomes accustomed to think of the parts 
with which he becomes acquainted as having a certain 
position in reference to the points of the compass, the 
child gradually builds up, as well as his idea of the 
directions of particular places, his notion of the cardi- 
nal points of the compass themselves. This is prob- 
ably done first with reference to some one place. The 
child becomes familiar with the fact that the sun rises 
in a certain direction and sets in the opposite direction 
with reference to his own home and the neighboring 
streets and buildings. He then, perhaps, acquires the 
idea of north with reference to the rising and setting 
of the sun and to the stars, etc. ; and after these general 



GEOGRAPHY 169 

notions have been acquired in connection with his 
home town, he appHes them to other towns and then 
makes the ideas more and more general. 

Imagination extends sight experience, as sight ex- 
tends touch experience. The development of orienta- 
tion, as it has been outlined, consists in the formation 
of ideas of the direction of objects or places with refer- 
ence to one's self, the development of the idea of dis- 
tances between objects and of the direction which one 
is from another, and of directions with reference to a 
standard direction. We have now to consider the re- 
finement of ideas of distances and directions between 
places and of the way in which these ideas are built up 
in some detail. When a person forms in his imagination 
the idea of places with which he is familiar and the dis- 
tances and directions between them, he is extending his 
experience in much the same way that we extend the 
experience which we get through handling objects and 
through our direct contact with them, when we not 
only touch them, but also see them. The blind man is 
very limited in the extent to which he can organize 
objects into a well-ordered whole. It is said that his 
ideas of objects in relation to one another, so far as 
they are clearly worked out, are limited by the amount 
that he can span with his arms, that is, by the extent 
of space from which he can get simultaneous sensa- 
tions. We can organize objects in a better manner 
when we experience them simultaneously than when 
we experience them one after another. We may think 



170 PSYCHOLOGY OF COMMON BRANCHES 

of the imagination as extending one's experience of 
space beyond that which is apprehended through per- 
ception, or through seeing objects, in much the same 
way in which sight extends the experience which we 
get through touch. To put it in another way, if a per-'** 
son lacked the ability to form an organized conception 
of different places in his imagination, he would be lim- 
ited, in comparison to the person who possesses the 
ability to develop orientation through his imagination, 
in much the same way that the blind man is limited in 
comparison with one who sees. This does not mean 
that the imagination supplies the place of seeing. The 
blind man can fill out through his imagination what 
he lacks through his vision. It serves merely as an 
analogy to illustrate the fact that we have different 
kinds of spatial recognition which are different in the 
range of objects or places which they can include. In 
the first place, we have the ability to recognize, 
through touch and movement, the form of objects and 
the position of objects which are within a very small 
range. Broader than this is the sense of sight, which 
enables us to recognize simultaneously wider ranges 
of objects. Still broader is the imagination, which 
gives us an orientation among places so widely sepa- 
rated that they cannot be perceived at the same time, 
even by sight. 

Imagination may be stimulated by the sight of a 
large district from a high place. The transition from 
sight to imagination in the development of orientation 



GEOGRAPHY 171 

may be bridged by taking the child to a high place, so 
that he can get a sight of a larger number of places 
than he ordinarily sees. This enables him, by means of 
the broad range of vision, to obtain a unified view of 
those places with which he has already become famil- 
iar. A child may be taken to a tall building or the top 
of a hill and given the opportunity to survey the, 
neighboring streets and buildings. He will then get an . 
idea of the whole, which he can hold in his imagination 
while he walks about upon the ground and while his 
vision is limited. He may be stimulated thus to keep 
in mind the location of places in his imagination by 
questions regarding the directions or distances of 
places from the place on which he stands, or by ques- 
tions regarding the direction of one place from another, 
or their distance apart. 

Maps and globes 

Maps are symbols which are interpreted by the 
imagination. This practice will prepare the way for 
the child to form the idea of the relation of places to 
one another, even though he has not seen them to- 
gether. This transition from sight to imagination is 
greatly facilitated by the use of maps. The child may 
draw his own map of a region which he sees from a 
high place, or the location of the places upon the map 
may be pointed out to him as he sees them from the 
eminence. The child is thus brought to the under- 
standing of maps as signs or symbols of the relation of 



172 PSYCHOLOGY OF COMMON BRANCHES 

places to one another. When he has learned through 
this means what a map is for, and what it refers to, 
he is able to use a map as a means of guiding his 
imagination in understanding the relationship of 
places which are so distant that they cannot be seen 
at the same time. 

Maps are necessary to insure accuracy in spatial 
imagination of large areas. It is possible to get only 
a very vague and rough idea of the location of widely 
separated places unless a map is used. Suppose that 
one should try to get an accurate idea of the relative 
location of three places by traveling from one to an- 
other. The three places might form the three apexes 
of a triangle. In order to form an accurate idea of 
their location, it would be necessary to keep in mind 
not only the direction in which one is traveling in 
going from one to another, but also the distances. If 
an error was made in either the distance or the direc- 
tion, it would introduce an error into the notion of the 
positions of the places w^ith reference to other places 
and with reference to one another. On the map, due to 
the fact that it is drawn to scale, the relative distances 
as well as the directions are represented to the eye. In 
attempting to get a clear notion of a region, one must 
either consult a map which has been made of it or 
make a map by means of compass and a measuring 
device. It is diflBcult for one who has been brought up 
to the early use of maps to imagine to himself the sort 
of orientation which a person would have who had 



GEOGRAPHY 173 

never used maps; but it seems clear that a person 
who does not have the assistance of maps will re- 
quire a much longer time to become oriented in a 
region than one who uses maps. 

After being first used in close relation to the con- 
crete, maps may be used abstractly. After the child 
has learned the meaning of maps by associating them 
with the regions with which he is familiar, he may 
learn to use them without referring directly to the 
actual world which is about him. It is not necessary 
that a person in planning a railroad journey shall at 
every moment think of the direction or the distances 
which are represented on the map as related to the 
place which he is occupying. He may be in one city 
and be planning a railroad journey which is to start 
from another city. In that case if he applies the map 
to the concrete world, it must be by imagining himself 
in the other place. It is very probable that we learn 
to use maps in a highly abstract way for such pur- 
poses, but, as in a great many other cases, the meaning 
of maps will be greatly restricted if they have not in 
the beginning been closely related to the actual world. 
It is, therefore, highly desirable that the child should 
begin by a study of the region in which he lives, and 
that he should learn the meaning of maps with refer- 
ence to this region instead of beginning with a map 
and attempting afterward to apply it to the real world. 

Should the child begin to study his neighborhood or 
the earth as a whole? This raises the question which 



174 PSYCHOLOGY OF COMMON BRANCHES 

is similar to the one which confronts the teacher of 
history, and that is whether the child studying geo- 
graphy should begin with those facts which are open 
to his observation and in his experience, and gradu- 
ally work to those which are more remote; or whether 
he ought to begin with the larger, more general facts 
and then fill in the details by his later study. In the 
case of geography there is, perhaps, more to be said for 
the position that one should begin with the broader 
facts. We may say that the child can best understand 
the world when he realizes that it is a globe and that 
it revolves about the sun, and rotates on its axis, and 
so on. These facts are necessary for the comprehen- 
sion of the seasons, for example. Furthermore, the 
child cannot understand the setting of the region in 
which he lives without knowing something of its rela- 
tionship to the larger divisions of the earth. 

Some home geography is necessary as a starting- 
point and basis for broader study. On the other hand, 
the general principle that the child's comprehension 
of general facts should be based on his experience of 
his immediate concrete surroundings holds in this case 
as in the case of history, — at least, up to a certain 
point. A map means nothing to a child unless he has 
first learned the relation of a map to the region with 
which he is acquainted. A globe means nothing to 
him unless he realizes that it is a representation of the 
earth upon which he finds himself. It is, therefore, 
necessary that he have at least so much of an acquaint- 



GEOGRAPHY 175 

anceship with his neighborhood that when he comes to 
study the more comprehensive symbols he shall know 
what they represent. This does not mean that he shall 
necessarily progress continuously from the narrower 
to the broader facts, but that he shall have a fairly 
complete experience with the narrower facts, so that 
when the broader ones are presented to him, they will 
have a clear meaning. 

The existence of the earth as a whole and of the 
heavenly bodies is brought home to the child in his 
everyday experience. The case of geography is a little 
different from the case of history. In the first place, 
the rest of the earth and the other bodies which are 
related to the earth are presented in some measure to 
the child's present experience. He sees the sun and the 
moon and he observes the sun rise and set. He can 
see the outline of the shadow of the earth upon the 
moon. Furthermore, the other parts of the earth than 
that which is within his immediate experience exist 
simultaneously with the parts with which he is ac- 
quainted; and although he does not have direct experi- 
ence with them, he meets references to them frequently. 
He may hear about a war which is taking place at some 
distant place, or be told of events which are occurring 
or have occurred in the past at other places. Perhaps 
he was born in another town from that in which he 
Hves, or even in another country, and he hears these 
places talked about. And so, in a variety of ways, he 
learns indirectly about other parts of the world than 



176 PSYCHOLOGY OF COMMON BRANCHES 

those which are in his immediate neighborhood. 
Again, the different parts of the earth are related to 
one another as a whole in a somewhat more intimate 
way than are the different periods of history. For 
these various reasons, then, it seems necessary to 
introduce the knowledge of the earth as a whole, and 
even of its relationship to the sun, the moon, and the 
other planets, as soon as the child has had sufficient 
concrete experience to give a meaning to the symbols 
which are used, — that is, to the maps and to the 
globe. 

Care is needed properly to associate directions on 
the map with the cardinal points. A difficulty with the 
understanding of maps sometimes arises from regard- 
ing a certain side of a map as representing the wrong 
direction in the concrete world. By convention we use 
the top of the map to represent north. This associa- 
tion must, of course, be formed in the mind of the 
child. It is probable that if his attention is not called 
particularly to the matter he will naturally associate 
the directions on the map with the directions on the 
earth corresponding to it as it lies upon the desk. That 
is, if the child faces the east or even if the map is on 
the east wall, and nothing to the contrary is said to 
him, he will think of the top of the map as represent- 
ing the east. We have no experimental facts Cn the 
matter, but observation by teachers seems to indicate 
that it is desirable at first, in order to form the proper 
association, that maps be placed so that the direction 



GEOGRAPHY 177 

on the map corresponds to the direction on the earth. ^ 
As the child becomes more accustomed to the use of 
maps, he can readjust his position in imagination, but 
at first the connections between the symbols and the 
facts is somewhat difficult for him to make at the best, 
and it should be made as easy as can conveniently be 
done. For this purpose maps which are drawn upon 
the earth itself — for example, a map of the school- 
yard made upon the playground or in the sand-box — 
is the type of symbol which can be most easily associ- 
ated in the mind of the child with the fact which it 
represents, and this is the step which is the most nat- 
ural to take first. 

Excursions accompanied by map-drawing assist the 
development of orientation. It goes without saying 
that excursions properly conducted greatly assist the 
child in the development of orientation. To be properly 
conducted, from the point of view of geography, means 
that the child shall during the excursion attempt to 
keep the directions and distances in mind, and that he 
shall draw a map of the region which is visited either 
during the trip or after the return. The fact that a 
person traverses a region does not mean that he has 
comprehended anything of the location of its parts. 
It is necessary that he himself actively observe the 
directions and distances in order that he may get any 
such notion. The leader is the one who knows where 
he is going and who can find his way about because 
he keeps directions in mind. A person who is not 



178 PSYCHOLOGY OF COMMON BRANCHES 

attempting to lead becomes easily confused. There 
should, therefore, be some motive, such as the neces- 
sity of drawing a map, which shall lead the child to be 
attentive to this feature of the experience. 

Summary. As was said at the beginning of the chap- 
ter, orientation is not by any means the whole of 
geography nor perhaps the most important part of it. 
It is the fundamental part, however, and without its 
proper development the other parts are much more 
difficult to learn properly. Physical geography and 
commercial geography are in the nature of natural 
sciences, and since we are not attempting to distin- 
guish between the different branches of natural science, 
the general principles which are discussed in the later 
chapter on this subject will apply to them, and may be 
taken as sufficient discussion of them for the purposes 
of this book. 

REFERENCES 

1. A. Binet: "Reverse Illusions of Orientation." Psychol. Rev. 
(1894), vol. I, pp. 337-50. 

2. C. H. Judd: Introdtiction to Psychology, chap. 6. Scribnera, 
1907. 



CHAPTER IX 

MATHEMATICS: ABSTRACT THOUGHT 

Number an abstract mental process 

In the mental processes and the forms of learning 
which have been discussed so far the responses have 
been governed in the main by the specific character 
of the objects which served as stimuli to them. In 
handwriting, the motor coordination is governed and 
directed by the specific form of the individual letters. 
In drawing, reading, and other forms of perceptual 
learning, the aim is to develop the recognition of 
objects in their particular character, and the facts 
which are significant concern the special characteris- 
tics of objects which distinguish them from others. 
Even in imagination, in which experience is extended 
beyond the concrete world which is present to the 
senses, the reference is still ultimately, in large meas- 
ure, to the nature of the world as it is presented in per- 
ception. The characteristics of objects in which in- 
terest and attention center are their " real " charac- 
teristics, even though they are represented indirectly 
in the imagination. In number we have to do with 
a mental process which employs concrete experience 
only as a starting-point. As soon as the number sym- 
bols have acquired a meaning through concrete experi- 



180 PSYCHOLOGY OF COMMON BRANCHES 

ence they become largely independent of it. How this 
abstract number idea develops we shall see in the 
following paragraphs. 

The child first distinguishes between one and two or 
between more and less. The stages by which the child 
comes to the full number idea are gradual. His earliest 
idea of number is probably the distinction between one 
thing and two things, or is little more than the distinc- 
tion between more and less. If he has two balls or 
playthings which are exactly alike, he knows when one 
of them is missing, and this appears to be the earliest 
manifestation of the recognition of the number of ob- 
jects. 

The number attitude is highly abstract. When the 
child uses number to the extent of counting, his atti- 
tude toward things undergoes a change. He regards 
things now merely as counters which are to be put 
together, and the interest is not in the things them- 
selves, but in the fact that they can be put together 
in thought to make larger or smaller sums. This atti- 
tude toward things as being counters rather than hav- 
ing an interest because of their individual characteris- 
tics is a typical number attitude. We describe it in 
technical terms by saying that in number the attitude 
toward objects is an abstract one.^ We are thinking 
only of one aspect of the objects, — that is, of their 

^ An abstract idea is one which does not merely reproduce the 
experience with concrete objects, but deals with one phase or aspect 
to the exclusion of the others. The use of language or other symbols 
makes possible such a high degree of abstraction that the symbols 
may have very little direct reference to the concrete world. 



MATHEMATICS 181 

multiplicity, or of how many there are, — and we are 
not concerned, so far as our interest is the number 
interest, in their size, weight, shape, use, color, or any 
other of their properties. 

The use of objects as counters is illustrated by the 
primitive herder. The use of objects as counters, 
which makes clear the abstractness of the number idea, 
is well illustrated by a practice which is occasionally 
employed by primitive people to make a record of the 
number of animals in their herd. Before counting has 
been sufficiently developed, so that there are enough 
number names to designate a good-sized herd, a prim- 
itive herder sometimes records the number of animals 
which he possesses by driving them through a stile 
and putting down a pebble for each one as it goes 
through. He then accumulates a pile of pebbles which 
corresponds in number to the herd. Each pebble 
represents one unit, and in the same way each sheep 
represents one unit; therefore, in this case the owner of 
the herd takes an abstract view of both the sheep and 
the pebbles. The sheep and pebbles do not resemble 
each other as concrete objects at all. They may not 
even be alike among themselves. The sheep may be 
large or small, young or old, with a plentiful supply 
of wool or a little supply; and the stones may be large 
or small, of regular or irregular shape and of various 
colors. In spite of the difference in all of these objects, 
however, they are all thought of as alike because they 
are regarded merely as counters. 



182 PSYCHOLOGY OF COMMON BRANCHES 

Counting also illustrates the abstractness of num- 
ber. The abstractness of number is also illustrated in 
counting. When the child gets sufficient command of 
the number names so that he can count readily, he is 
very much interested in counting all sorts of objects. 
He may count the buttons on his shoe, the chairs in 
the room, the houses in the block, or the trees in the 
yards, and so on. In thus applying the number names 
to a great variety of objects it becomes clear that he 
regards these objects, not from the point of view of 
their concrete character, — that is, of their use or their 
appearance or any other quality which leads one or- 
dinarily to classify objects together, — but that he 
regards them in the highly abstract character of units 
or counters. In the application of any other names 
there is a more intimate similarity between the objects 
which are grouped together. Tables have in common 
the flat tops which we use for setting things upon; 
chairs have in common the fact that they are used to 
sit upon; and so on; but the objects which are counted 
have nothing in common but the fact that they are for 
the moment regarded as units and that they are put 
into a series of groups to which are applied the num- 
ber names. The same number names may be used in 
counting any objects whatever. 

Number names or counters are symbols. The illus- 
trations which have been given of the simple use of 
numbers bring out one of the fundamental character- 
istics of numbers. In both cases a series of objects is 



MATHEMATICS 183 

represented by a series of other objects which stand 
for them as signs or symbols. When the stones are 
used as representatives of the sheep, they are thought 
of only as symbols of the sheep and of merely the 
number of sheep. When the number names, "one," 
"two," "three," etc., are used to designate objects 
they stand as a sign or symbol of the number of the 
objects, each being regarded as one unit. 

The early development o/ the number idea 

There is a one-to-one correspondence between sym- 
bols and objects. In both these cases there is one sign 
or symbol for each object which is counted and there 
is one object for each of the symbols which is used. 
This correspondence is called a "one-to-one corre- 
spondence." It has been illustrated by Royce in the 
example of horses and their riders. If there are a group 
of horses and a group of riders, we pair them off by 
giving one horse to each rider and one rider to each 
horse. If there are any of one or the other left over, it 
indicates that there are more of one than of the other. 

The child does not at fibrst apply this principle in 
counting. This one-to-one correspondence is such a 
simple and fundamental matter that it may seem un- 
necessary to mention it. The child, however, does not 
grasp it when he first tries to count. If one watches 
the early beginnings of counting, one will see that the 
child frequently points to a number of objects to corre- 
spond to a single number name or uses several names 



184 PSYCHOLOGY OF COMMON BRANCHES 

for one object. He has not grasped the notion that 
one name must be given to each object and that each 
object must have its name in order that the final num- 
ber name shall represent the number of the objects 
which have been counted. 

What is taken as a unit depends on the purpose in 
counting. It is worth while emphasizing that for the 
application of this one-to-one correspondence which 
is represented by counting, as well as the other forms 
of number into which it develops, it is not necessary 
that the objects used as units ^ be all of the same kind. 
We may count together any things which we choose 
to think of as units. In this case we do class them 
together sufficiently to put them into the same group. 
For instance, for the purpose of counting one may 
class together chairs, tables, beds, couches, etc., when 
the purpose is to count all the articles of furniture in 
the house. The influence which the purpose that the 
individual has in mind has upon the objects which he 
regards as units may be illustrated further in the case 
of counting all of the trees in a certain area, say an 
acre. In this case one will count every growing thing 
which is called a tree. One might, however, wish to 
count, not all of the trees, but all of a certain kind, as 
beech trees or pine trees. In this case the unit which is 
selected is of a more restricted nature. This is what is 

^ A unit is anything which for the time being is taken as single 
for the purpose of pairing, counting, grouping, or any of the number 
operations. 



MATHEMATICS 185 

meant by saying that we may choose to call anything 
a unit which for the time being we choose to put into 
a certain group or class. 

The idea of quantity implies similar units. The dis- 
tinction should be made between number, in which the 
multiplicity of units is the chief idea and the concrete 
nature of the units is not important, and quantity, in 
which there is included also a different idea. We apply 
the idea of quantity to such matters as the amount of 
water in a tank, or the number of acres in a field, and 
so on. In other words, we use the term "quantity" 
to designate the number of identical units which exist 
in a certain total amount of material. To illustrate 
the difference from the example which was cited above, 
we find the number of trees by counting, and in this 
case a small tree counts for as much as a large tree. If 
we wish to find out the quantity of lumber in an acre 
of forest, however, we take as the unit a foot or a 
thousand feet of lumber, and calculate how many of 
these similar units there are in the grove. In this case 
every unit is the same as every other unit and the same 
number of units will always express the same quantity 
wherever it is found. 

Early number is related to the fingers. The con- 
sideration of the act of counting, which is the applica- 
tion of the one-to-one correspondence by applying a 
series of number names to a series of objects, leads us 
to the question of the origin of the number names, and 
of the development of the understanding of number 



186 PSYCHOLOGY OF COMMON BRANCHES 

names in the child. We have clear evidence that num- 
ber names were often first developed through counting 
on the fingers. In fact, the word which we use to desig- 
nate a single number symbol, " digit," indicates that 
the fingers had a close relationship to the early devel- 
opment of number. Further evidence that counting 
was developed through the use of the fingers appears 
in the decimal system, in which the number of the 
fingers forms the basis of grouping. We shall learn 
more particularly about this in a later paragraph. 

The number names may originally have represented 
position in a series. In the character of the early 
names of specific numbers there is clear evidence of the 
origin of numbers from counting on the fingers. »In 
the case of some primitive tribes, furthermore, the 
number names are the names of particular fingers and 
not merely of any of the fingers indififerently. This 
indicates that the fingers were counted in a certain 
fixed order and suggests that possibly the earliest 
number idea was one of a position in a series rather 
than of a group of objects taken all together. 

Two illustrations of the use of names of particular 
fingers as number names follow. 

The Hudson Bay Eskimos use the following number 
names: ^ 

8. hittukleemoot = middle finger (of second hand) . 

9. mikJceeluJckamooi = fourth finger. 
10. eerkilkoka = little finger. 

* L. L. Conant: The Number Concept. Macmillan, 1896. 



MATHEMATICS 187 

The Jiviros of South America had the following 
names : — 

5. alacotegladu = one hand. 

6. intimutu = thumb (of second hand). 

7. tannituna = index finger. 

8. tannituna cabiasu = finger next to the index 
finger. 

9. bitin otegla cabiasu = hand next to complete. 
10. catogladu = two hands. 

Number names mean to the child, at first, position 
in a series rather than a group of objects. However 
this may be in racial development, it appears to be the 
natural order of development in the child. As the 
child is taught number by the common method of 
counting on the fingers, he at first thinks of each num- 
ber name as being the name of one of his fingers. The 
name does not at first include all the fingers in the 
series up to the one in question, but merely the one 
which has been reached at the time when the name is 
spoken. In other words, the first idea that the child 
gets from counting is the ordinal rather than the car- 
dinal idea. The numbers mean to him first, second, 
third, fourth, and so on. After he has learned to count 
the same series of objects in different orders, or to 
count other things than fingers, he gradually comes to 
realize that numbers represent a whole group of ob- 
jects rather than one object which has a certain posi- 
tion in a series. 

Our number system is based on a grouping by tens. 



188 PSYCHOLOGY OF COMMON BRANCHES 

Before the child has proceeded very far in learning to 
count, he comes upon a very significant fact in our 
number system. This fact is that we have enough dif- 
ferent number names to extend only a small way in 
the number series. We employ only ten different 
digits. As has been mentioned already, this is related 
to the fact that we have only ten digits on our hands. 
When we get to the end of this number of digits, we 
do not add other names, but begin over again, using a 
sufficient modification of the names to indicate that we 
are repeating the series a second time. When we have 
finished with the series a second time, we begin and go 
over it the third time, with a modification which is 
derived from the second digit, which indicates that 
this is the second time the series has been duplicated. 
The name and the symbol for twenty are directly 
related to two, and thirty to three, and so on. 

This system of grouping reflects our inability to com- 
prehend more than a small number of ungrouped ob- 
jects. The limitation of the number of entirely distinct 
number names is due to another fact besides the 
origin of number in connection with the fingers. This 
fact is that the number of objects which we can hold 
in mind at the same time is limited. It is impossible 
for us to achieve an immediate and distinct recogni- 
tion of a large number of objects unless we divide 
them into groups. This is precisely what we do by our 
system of number names. When we get beyond a 
number which constitutes the limit of a manageable 



MATHEMATICS 189 

group, we begin a new group, and then designate it 
as being a second one. It is as though the primitive 
herder, in laying aside pebbles for his sheep, should 
put them into one group until he had got as many as 
he could grasp mentally at once, and then begin a 
second group. 

The choice of ten as the unit of grouping is not the 
best possible. The name " decimal system " indicates 
the number of digits which are included in each group. 
It can be shown that it would be better, from the 
standpoint of the use of numbers, to take a different 
number for the unit group. Instead of using ten, 
twelve would be a more manageable number, because 
it has a larger number of factors. Ten can be factored 
only by two and five, whereas twelve can be factored 
by two, six, three, and four. It was an accident due to 
the fact that counting grew out of the use of the fingers 
that ten forms the basis of our system. 

The grouping system facilitates the number opera- 
tions. This division of numbers into manageable 
groups is of value not only because it enables us the 
better to grasp the meaning of larger numbers, and 
facilitates the systematic development of number 
names without extending the number of different 
names indefinitely, but also because it facilitates the 
processes of addition, subtraction, multiplication, and 
division. In adding the numbers twenty-three and 
forty -four we do not attempt to comprehend the com- 
bination of the two numbers as composed of single 



190 PSYCHOLOGY OF COMMON BRANCHES 

units, but first add the single units which compose the 
fractional parts of the groupings, namely the three 
and four, and then combine the two larger groups; 
and finally obtain the result by combining the units 
and the larger unit groups. If the number is such that 
the sum of the single units come to more than ten, the 
excess above ten is put into the result as units and the 
group of ten is added to the other larger groups. 

Grouping creates the distinction between higher 
and lower units. What the decimal system amounts 
to, as this illustration shows, is a method of using num- 
bers to indicate the different kinds of units. By this 
means we may regard a digit as representing either a 
single unit or a group of these units. In our decimal 
system the group which can be represented as a higher 
unit is composed of ten of the lower units. 

The distinction between higher and lower units is 
expressed clearly in our notation system. This dis- 
tinction between a higher and lower order of units is 
most easily grasped by the use of the written numbers 
for illustration. The group system may be used for 
calculation even though it is not expressed in the nota- 
tion by written numbers. The decimal system was 
used in Roman times in manipulating calculating 
machines similar to the abacus, while the written num- 
bers were expressed in the clumsy Roman notation. 
A written number notation, which shall express the 
decimal system adequately, must represent in some 
manner the fact that a digit may stand for a single 



MATHEMATICS 191 

unit or for a group unit, that is, for a lower or a higher 
unit. It is a commonplace with us that this is done by 
having only ten signs and using the same sign to ex- 
press by its position either a single unit or a group of 
units. When we think of the application of the deci- 
mal system in calculating, then, we inevitably picture 
it in mind as expressed by numbers, and think of bor- 
rowing and carrying, for example, as they are worked 
out by our so-called Arabic notation. 

Other experiences besides counting assist the child's 
development in number. These illustrations of the 
application of the decimal system have taken us some- 
what ahead of the development of the child. We have 
seen that counting gives the child first the idea of 
position in a series and that he can by counting pro- 
ceed to the recognition or the manipulation of fairly 
large numbers. He may by this means, it is true, 
recognize cardinal numbers, but the elaboration and 
perfection of this recognition can be carried out more 
easily by the addition of certain other forms of expe- 
rience. 

The idea of number develops out of experience with 
concrete objects. There has been considerable differ- 
ence of opinion as to the kind of concrete experience 
which is best suited to the development of the idea of 
number in the child. It is well recognized that some 
experience with things is necessary at the beginning, 
to develop the early stages of the number idea, before 
it has become highly abstract. While the number idea 



192 PSYCHOLOGY OF COMMON BRANCHES 

is not complete until it has become independent of the 
thought of any concrete things, yet it is developed 
first through the experience of the child with concrete 
objects. 

Measurement of quantity, or grouped objects, may 
be used to give concrete basis for number. The two 
forms of experience which are commonly used to carry 
the child beyond the counting stage are measurements 
of length or of area or of cubic contents; and grouped 
objects, as marbles or balls or sticks. The measure- 
ment of objects means the dividing of an object into 
equal units and then the determination of the quantity 
of the object by calculating the number of the units 
into which it is divided. When the length of an object 
is to be measured, the calculation of the quantity is a 
simple matter of the application of a measure unit to 
the object. When an area is measured, the child may 
conceive it as composed of the small squares which 
may be used as units. The measurement of volume is 
still more complex. When sticks, or marbles, or balls 
on a frame are used, each unit is represented by a 
different object, and the combinations of numbers, 
their manipulation, and various operations may be 
illustrated by grouping these objects. The fundamen- 
tal laws of number may be represented by the different 
ways in which a group of objects may be broken up 
into smaller groups, and then may be arrived at again 
through combining these smaller groups into the larger 
group. 



MATHEMATICS 193 

Both methods may be used in combination to advan- 
tage. While divergent views may be held as to the 
value of the two forms of concrete experience which 
may be used in teaching the early numbers, it is not 
necessary that we choose either to the exclusion of the 
other. Each has its own advantages, and one may 
very well be made to supplement the other. The situa- 
tion is not the same as it is in the case of some other 
differences of procedure in education which are mutu- 
ally contradictory. It is probably desirable that more 
than one method be used in order that the child may 
the more readily handle the number processes inde- 
pendently of concrete material. If he learns with ref- 
erence only to one kind of objects, he may find it 
necessary to refer to this one object in making his reck- 
oning, but if he uses now one and then another he is 
more likely to become independent of both. 

Grouped objects illustrate the decimal system par- 
ticularly well. There are many number processes or 
ideas which may be illustrated conveniently by the 
method of grouped objects. One of these is the deci- 
mal system. The decimal system is primarily one of 
grouping. In it we set aside a certain number of units 
and regard them as units of a higher order. In using 
grouped objects this may be represented by counting 
ten and then setting these aside as a group, and then 
counting ten more and setting them aside, and then 
regarding as units the groups which are themselves 
made up of smaller units. 



194 PSYCHOLOGY OF COMMON BRANCHES 

Number operations may be expressed as forms of 
grouping and regrouping. This grouping method may 
also be well used to illustrate the aspect of number 
which Judd has dwelt upon in his chapter on "Num- 
ber" in Genetic Psychology for Teachers. It is there 
pointed out that the number operations may be de- 
rived from the fact that if a group be divided up into 
a variety of groups, these groups when recombined 
always give the original number. For instance, if 
we take a group of twelve objects we may divide it 
into two groups of six each, into three groups of four 
each, etc. After the division has been made, we may 
recombine the smaller groups again and always 
get the original twelve. In other words, the total 
number always remains the same whatever the group- 
ing. 

Grouping is a convenient means of teaching the fun- 
damental operations. This is the basis of the under- 
standing of the processes of division, multiplication, 
subtraction, and addition. The child by manipulating 
a group of objects may readily learn the various ways 
in which it may be broken up into smaller groups. For 
example, he may readily find that twelve may be 
broken up into three groups of four each, or four 
groups of three each, or two groups of six each, or six 
groups of two each. This is probably a more direct 
way of learning these facts than is measurement, 
though the same facts may be learned through the 
other method. Grouped objects are more easily ma- 



MATHEMATICS 195 

nipulated than are units of length or of area, on ac- 
count of the ease with which one may break up a 
group in a variety of ways and see the way in which 
the units may be recombined. The objects are more 
flexible and can be modified more readily than quan- 
tities which are suitable for measurement. 

Measurement makes less prominent the units, but 
more prominent the size of the whole number. The 
use of measurement to make concrete these same proc- 
esses may be illustrated. If a stick is measured into 
inch lengths, the child may count the inches two at a 
time and see that he has six, or may count the sixes 
and see that he has two. In the same way, he may 
divide the total length into three groups of four, or 
four of three each. Measurement makes more promi- 
nent the quantity as a whole than it does the individ- 
ual unit, and it would seem to require a greater ability 
in abstraction on the part of the child to get a clear 
notion of the unit in this case, as compared with the 
use of distinct objects as units. From another point 
of view measurement is particularly suitable, since it 
calls the child's attention particularly to the size of 
the number as a whole, and is therefore useful in 
enabling him to see clearly the relative size of two 
numbers. If he has a stick twelve inches long and 
another six inches long, he may measure them and 
then, comparing the length of the two sticks with his 
eye, get a notion of the relation between the number 
six and the number twelve. We shall return to this 



196 PSYCHOLOGY OF COMMON BRANCHES 

matter of the learning of the fundamental processes 
in later paragraphs. 

Grouping is conveniently illustrated by the means of 
the abacus. The use of grouped objects to illustrate 
the simple number processes has been developed in 
the apparatus which is called the "abacus." This is a 
frame containing a series of parallel wires upon which 
are strung wooden balls capable of being moved back 
and forth. This instrument was formerly used widely 
in the United States, and there is a revival of this or 
some similar device at the present time. It has been 
developed in more complicated forms in Europe and 
is there used extensively. 

In general we teach the meaning of numbers and 
their operations before teaching their symbols. The 
procedure which has been described assumes that the 
child learns to understand about numbers before he is 
taught to go through the formal processes of reckoning 
with figures. In the very beginning the child has some 
comprehension of the meaning of " one " and " two." 
He does, it is true, usually learn to count by a mechan- 
ical repetition of the number names before he has 
developed the understanding of the meaning of the 
different numbers very far, but, after this has been 
done, we commonly teach him the meaning of numbers 
through concrete objects before he learns to write 
them. Further, he learns the processes of addition, 
subtraction, multiplication, and division before he 
learns to use the plus, minus, multiplication, and divi- 



MATHEMATICS 197 

sion signs; and he learns what it means to combine 
numbers and express their equivalence to a larger 
number before he uses the sign for equality. In general, 
the understanding of the process in concrete terms 
comes before the ability to express it in written figures 
and signs. 

Teaching the s3mibols formerly preceded the teach- 
ing of the number fact. This order of procedure, in 
which the child learns the meaning of the number 
operations before he is taught how to express them, 
has not always obtained in teaching practice. In the 
early part of the nineteenth century a revolution took 
place in the method of teaching arithmetic in the 
United States. Up to this time the child had been 
first taught to write the figures and to go through the 
various operations with figures in a mechanical way. 
He learned as a matter of rote memory that four and 
five make nine, and learned by the same method to 
put the figures down in the proper way. It was not 
believed that it was possible for him to understand 
why he put down nine rather than eight or ten, or at 
any rate, it was not realized that it was a desirable 
thing that he should understand the process before he 
learned to carry it out. 

Except in the beginning, mathematical operations 
are still frequently learned without an understanding 
of the reasons for them. The same difference in the 
method of teaching still runs through the higher 
branches of mathematics as well as arithmetic. It is a 



198 PSYCHOLOGY OF COMMON BRANCHES 

possible mode of procedure, and one which is often 
actually practiced, to cause the pupil to learn the 
various algebraic formulae, and to apply them, with- 
out any clear conception of what they mean. When 
the student comes to geometry, the demonstrations of 
the theorems are sometimes learned without any 
understanding of their meaning in terms of the figures 
which illustrate them. In arithmetic an illustration of 
the more complicated form of problems may be taken 
from the extraction of the square root. This may be 
taught in such a way that the pupils learn merely 
what to do next and how to proceed with the figures, in 
which case it becomes merely a sort of juggling feat. 
On the other hand, by the use of an appropriate figure, 
pupils may be taught, to some extent at least, to realize 
why they go through the various steps. 

The question as to which of these methods should 
be pursued is one which arises early. When we come 
to the borrowing and carrying operations, as in sub- 
traction and addition, and particularly when we come 
to long division, we have cases in which the form of 
procedure is rather complicated, and in which it may 
be plausibly argued that it is unnecessary and a waste 
of time to attempt to give the pupil an understanding 
of the reason for the performance of each step in the 
process. 

In general, the more clearly the pupil understands 
what he does the better. The detailed answer to this 
question may be left to the discussion of methodology. 



MATHEMATICS 199 

but at least we may say as a matter of general princi- 
ple that it is highly desirable to develop in the pupil 
ability to understand what he does in contrast with 
the habit of carrying on a process in a mechanical way. 
The history of the development of number teaching 
has indicated that a pupil can be led to understand 
very much more than used to be required of him. 
While there may be details of some of the processes 
which it is not practicable to enable him to understand, 
he should at least know what he is aiming at, and have 
a general understanding of the reasons for the proce- 
dure which he takes. The question may be left open as 
to whether this understanding can be or should be 
made complete. It probably will be found that the 
procedure must be somewhat varied to suit the vari- 
ous capacities of the different children. Some, who are 
rather dull, may not be able to understand the pro- 
cedure without too much time being spent or possibly 
even when an indefinite time is spent; and yet it is 
desirable that pupils should have a sufficient command 
of the simpler number operations to use them in 
practical life. On the other hand, for the pupil who 
is above average ability it is highly desirable that 
he shall acquire the habit of understanding clearly 
everything that he does. This is one of the most valu- 
able attitudes of mind for a person who is to advance 
beyond the most elementary stages of intellectual 
achievement. 

The understanding of the number processes must 



200 PSYCHOLOGY OF COMMON BRANCHES 

be supplemented by drill in performing them. While 
there is danger of erring on the side of making the 
learning of the pupil too mechanical and of neglecting 
to cause him to understand the process which he car- 
ries on, there is also a possibility, and even danger, of 
erring on the opposite side. There is danger of assum- 
ing that after the pupil has understood the procedure, 
he has gained all that he needs to gain from that topic. 
This is altogether a mistake. We have, up to the most 
recent years, reacted against the use of drill as a means 
of developing in the pupil the ability to perform in an 
efficient way certain simplc^activities. We have al- 
ready referred to this matter in connection with spell- 
ing. The same fault has been seen also in work with 
numbers. There has recently been a reaction against 
this neglect of drill and an emphasis upon the neces- 
sity of the pupil's being able to perform quickly and 
easily certain simple operations. We may merely 
repeat here the statement that to understand a process 
is not sufficient to enable the pupil to carry it out as he 
should. The effort to recollect how a process is to be 
carried on, or what the meaning of a problem is, makes 
the process slow and difficult. On the other hand, if 
sufficient practice has been undertaken so that as soon 
as the problem is presented the result comes to mind, 
or, if it is a longer problem, the mode of procedure 
comes to mind quickly, much time and energy are 
saved. There should be sufficient drill in all the proc- 
esses that the child is likely to have need for in his 



MATHEMATICS 201 

practical living to enable him to carry them on with- 
out hesitation and without making an undue number 
of mistakes. 

The development of the arithmetical operations 

The best order of teaching addition, subtraction, 
etc., is a matter of debate. Another question of pro- 
cedure, the solution of which rests upon the analysis 
we make of the number operations, concerns the order 
of teaching the fundamental operations, — addition, 
subtraction, multiplication, and division. The tradi- 
tional method is to teach addition, subtraction, multi- 
plication, and division in the order named. There is 
some ground, however, for thinking the order should 
be reversed, and that we should begin with division 
and multiplication and then proceed to subtraction 
and addition. We may examine the grounds for these 
two forms of procedure and attempt to determine 
which one of them is the better adapted to introduce 
the child to the complexity of the number processes. 

Multiplication and division involve the equality of 
the smaller groups. We may first contrast addition 
and subtraction taken together, with multiplication 
and division. Addition and subtraction differ from the 
other two processes in that in them we deal with un- 
equal groups. When we separate a group into a num- 
ber of smaller groups, in division, we obtain groups 
which are of equal size. In the same way, when we 
multiply, we take the same group a number of times 



202 PSYCHOLOGY OF COMMON BRANCHES 

until we arrive at the larger group which results from 
this multiplication. This fact of the equality of the 
groups in multiplication and division would seem to 
make these processes simpler than those of addition 
and subtraction. 

Addition and subtraction are probably simpler to 
the child. On the other hand, addition and subtrac- 
tion may be carried on one step at a time, as when we 
have four and add one to it, or when we add two to 
four. In this case it is necessary to keep in mind the 
first number and the number which is added and the 
resulting number. When we multiply, we have to keep 
in mind the number of the smaller groups, the number 
of groups which are taken, and the final result. To 
the adult who is familiar with the result of such a com- 
bination it seems to be fully as simple an operation as 
is that of addition. But it is doubtful whether the 
child who is learning the meaning of multiplication 
and division in the first place can readily jump from 
the idea of a certain number of equal groups to their 
combined number. He, in all probability, has to pro- 
ceed by taking one group at a time and calculating the 
result by the addition of each succeeding group to the 
preceding ones by a process of counting. The idea of 
the equality of the groups, then, is in reality a compli- 
cating element which makes the whole process more 
difficult. The same line of reasoning applies to divi- 
sion. The child probably has to approach the process 
by taking away one group at a time and counting the 



MATHEMATICS 203 

remainder instead of by making a division into several 
groups all at once. It appears from observation that 
he begins multiplication or division by counting and 
that he arrives at the result first without using the 
idea of the equality of the groups. This procedure will 
be sufficient in addition and subtraction, but in order 
to understand multiplication or division he must have 
grasped the fact also that the groups are equal. 

To take addition before subtraction seems to be in 
harmony with the child's habits. The further question 
may be asked whether we should take subtraction 
before or after addition, and division before or after 
multiplication. Here again the traditional method has 
been to begin with addition and multiplication and 
then go to subtraction and division, but there has been 
some disagreement with reference to this practice. In 
the case of addition and subtraction, the child clearly 
has the habit more firmly fixed of proceeding from a 
smaller to a larger number than a habit of proceeding 
from a larger to a smaller number. This is true in the 
ease of counting, and it is illustrated by the fact that it 
is very much easier for the child to count forwards 
than backwards. So far as the manipulation of grouped 
objects is concerned, it is of course easy to take several 
objects from a larger number and determine how many 
there are left, but, on the other hand, it is just as easy 
to add a number of objects to a smaller group and 
count the number which results. 

Division presents more possibility of difficulty than 



204 PSYCHOLOGY OF COMMON BRANCHES 

multiplication. There is a more radical difficulty which 
attaches to the process of division as contrasted with 
multiplication. This difficulty is due to the fact that 
not all numbers can be factored and that numbers 
which can be factored have only a few factors. The 
child can be taught to divide first by using only the 
numbers which have factors and using only those fac- 
tors which result in no remainder. Here again, how- 
ever, there seems to be no greater difficulty for the 
child in putting together the series of equal groups and 
determining what the result is than in dividing a 
larger group into a number of smaller groups and 
determining the size and number of each smaller group. 
Since there are greater possibilities of difficulty in 
division, it seems to be the better plan to defer this 
process and begin with multiplication. 

Multiplication and division introduce the principle 
of ratio. This description of multipHcation and divi- 
sion shows that they involve the idea of ratio, or at 
least the idea of ratio may be developed from them. 
When the child recognizes the fact that a number — 
as, for example, six — may be divided into three 
groups of two units each, it is but another way of 
looking at the same fact to say that two is one third 
of six. That three twos are six, and two is one third of 
six, may be presented as different ways of stating the 
same fact. There is no need of making the matter 
mysterious or difficult by any discussion of the ratio 
idea in the simpler number processes, as is sometimes 



MATHEMATICS 205 

done. It may be said that the idea of number involves 
the idea of ratio from the start. The idea of four is 
imphcitly four times one, and the idea of the unit is 
impHed in the idea of the number, but to discuss this 
matter with children is to attempt to call attention 
to a matter that is entirely taken for granted, and 
this raises a serious diflSculty. The idea of ratio, then, 
comes in most naturally when the child deals first with 
multiplication and division. 

Ratio may be represented by grouped objects or by 
measurement. This ratio idea may be very readily 
represented by the use of grouped objects. If objects 
are arranged in a regular fashion, — for example, if six 
objects are arranged in three groups of two each, — 
we have a very simple and easy mode of representa- 
tion of the idea that two is one of three groups which 
make up six, or is one third of the group. The ratio 
idea may also be represented by measurement, and 
for the simpler ratios this is, perhaps, somewhat more 
direct and easily grasped. The traditional illustration 
of a pie which may be divided into three or four or 
more parts is apropos in this connection. 

Fractions are merely symbols to express ratio. In 
explaining the method of representing fractions in 
number rotation, it is possible to make unnecessary 
difficulties for the child by going into too much minute 
detail. The first association may be merely between 
the term " one third " and the symbols of the one and 
the three expressed as a fraction. When we go further 



206 PSYCHOLOGY OF COMMON BRANCHES 

to explain what the one and the three mean, it may be 
explained that the numerator refers to the number of 
groups which are represented in the fraction and that 
the denominator refers to the number of groups in the 
total number which is represented. 

Operations with fractions are easily illustrated with 
grouped objects. In the operation with fractions, such 
as in addition of fractions, grouped objects are prob- 
ably more readily 
applied than 
measurement. All 
that is necessary 
in this case is to 
represent both ra- 
tios as a part of 
B O O O [OOP total groups of the 

same number of 

no. 10. ILLUSTRATION OF THE USE objCCts. IhlS IS 
OF GROUPED OBJECTS IN NUMBER fUp nnnnrr^if^ mnH*» 
OPERATIONS couciete moue 

of representing the 
reduction of the fractions to a common denominator. 
An illustrative case is shown in the accompanying figure. 
In order to add three fourths and one sixth we may let 
both fractions be represented by the appropriate part 
of the larger group of twelve. In the one case this 
group of twelve is divided into four groups and in the 
other case into six. If we then take three of the first 
division and one of the second, we can determine what 
our result will be by merely counting the number of 



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MATHEMATICS 207 

units in the various groups. Some such concrete 
method is undoubtedly desirable to give the child an 
understanding of the meaning of fractions and of the 
operation with them. 

Percentage is a special case of fractions. Percent- 
age is merely the extension of the principle of fractions 
to a special case and the use of a special means of 
representing these fractions. After the child has 
grasped the decimal form of grouping, as it exists in 
our number system, he is prepared to understand that 
percentage represents a case of fractions in which the 
denominator is ten or a multiple of ten. Expressed in 
concrete terms, this means that the whole group, of 
which the fractional part is represented in a percent- 
age, is always made up of ten, one hundred, or another 
multiple of ten. 

Decimal notation applies to fractional parts of a unit 
the principle we have already considered. In a similar 
fashion our mode of representation of percentage may 
be grasped as an extension of the mode of representing 
whole numbers. The child has already got a notion of 
the meaning of the places in writing a number, and 
understands that the digits in the first place represent 
single units, those in the next place to the left represent 
higher units each of which is a group of ten, and those 
of the next place a higher unit each of which is a group 
of one hundred, and so on. If we now extend the num- 
ber system to the right of the units place, we have a 
series of representations of fractional parts of a unit. 



208 PSYCHOLOGY OF COMMON BRANCHES 

In particular, if we suppose that the unit as represented 
in the units place be divided into ten parts, then the 
number in the next column to the right represents the 
number of these parts which are designated. The 
number in the next place represents a division in a like 
manner of each unit of the first decimal place into ten 
smaller units, and so on. Or if we start with the right 
end of any number, whether it include decimal places 
or not, each place to the left represents a unit which is 
ten times the unit represented by the next number to 
the right. 

Decimal notation is easily illustrated by grouped 
objects. These various units of higher and lower 
orders, and their significance in the different places of 
the number notation, may be represented by using 
grouped objects, as has been suggested. If we use 
grouped objects to represent decimal fractions, we 
start out by making the units which are represented 
in the first or units place, not single objects, but a com- 
posite unit, or a group. The child has become familiar 
with a composite unit from the earlier familiarity 
which he has with the meaning of the tens, hundreds 
place, etc. If the first place, then, represents a unit 
made up of ten parts, it may be clearly seen that the 
next place to the right — that is, the first decimal 
place — will represent a number of these smaller units 
which are of the lower order. 

The diflSculty of grasping the number idea and its 
mode of representation should be separated in order 



MATHEMATICS 209 

that the child may understand as much as is practi- 
cable. We have here brought honle to us a fact which 
was referred to earlier, namely, that the child is con- 
fronted with two sources of difficulty in his study of 
number. He is required not only to understand the 
number relations themselves, but also the means by 
which they are represented by the number symbols. 
Very frequently the difficulty which he has is mainly 
with the symbols. This emphasizes the conclusion 
that the two difficulties should be separated to the 
extent that the child should grasp the idea first in its 
concrete form, and then the mode by which it is repre- 
sented through the number symbols, making the con- 
nection between the two. When he starts with the 
number symbols they are meaningless to him, and he 
has no clue to the understanding of their complexities. 
The only course which is open to him, in this case, is 
to memorize the processes by rote memory and trust 
solely to his memory to guide him. Thus mathematics, 
instead of being a means of the development of think- 
ing, becomes merely a blind, mechanical exercise of 
memory. This is unfortunate and is to be avoided as 
far as may be. 

The menial processes in algebra 

Algebra is a further development of arithmetic. Up 
to this point we have traced the development of num- 
ber into more and more complex forms so far as it is 
included in the phase of number which we call " arith- 



210 PSYCHOLOGY OF COMMON BRANCHES 

metic." In the common-school practice this has been 
marked off sharply from another form, which we call 
" algebra." In reality the two are not radically differ- 
ent, but algebra is merely an advance over arithmetic 
in the same direction. Algebra is fundamentally like 
arithmetic in that it represents relations of numbers to 
one another. It differs, it is true, as we shall see, but 
the difference is not such a complete one that it is 
necessary to separate the two into entirely different 
subjects of study. As a matter of fact, it is desirable 
to introduce some of the algebraic forms of procedure 
into the later stages of arithmetic. 

Illustration of the arithmetical and algebraic meth- 
ods of solving the same problem. We may first make 
clear the relation of algebra to arithmetic, as well as 
the difference between them, by an illustration; and 
then discuss the meaning of this difference more par- 
ticularly on the basis of this concrete example. The 
following example may be worked either by an arith- 
metical form of procedure or by using an algebraic 
method. It is an example given by D. E. Smith in 
The Teaching of Arithmetic , page 74. The problem is: 
"If some goods are sold for $1,012.50 at a profit of 
12^ per cent, what did they cost? " 

The common method of solving this problem accord- 
ing to arithmetic is to let 100 per cent represent the 
cost and 100 per cent plus 12§ per cent, or 112| per 
cent, represent the selling price. Then, dividing 
$1,012.50 by 1.12|, we have as a result $900, which 



MATHEMATICS 211 

represents the cost. This form of procedure will give 
the answer, but it is difficult to make the child under- 
stand why it is taken. Why do we let 100 per cent 
represent the cost, and why do we divide $1,012.50 
by 1.12^? It is difficult to make the child recognize 
that this is more than an arbitrary procedure. 

The other procedure is to let some letter, such as 
c, represent the cost. This is a natural letter to take, 
since it is the first letter of the word. Then the selling 
price is c plus 12^ per cent of c, since the profit was 
12^ per cent reckoned upon the cost. The selling price 
then is 1.12^ c. This in terms of the equation becomes 
1.12^ c = $1,012.50. 

The equation may then be solved by dividing both 
terms by 1.12|, when we get as a result — 
c = $900.00. 

By using illustrations from concrete numbers the 
procedure of dividing both terms of the equation by 
the same number may be justified without going into 
a full explanation of it at this time. 

The symbols of algebra are more abstract than those 
of arithmetic, since they do not represent definite 
numbers except as they are defined by other elements 
in a problem. This method of solving a problem illus- 
trates the essential advance of algebra beyond arith- 
metic. In arithmetic, each symbol, such as the sym- 
bol 5, represents a definite number. Each number 
may be illustrated by reference to various kinds of 
concrete objects. It is abstract in so far as it may be 



212 PSYCHOLOGY OF COMMON BRANCHES 

applied to any sort of objects which we choose to 
regard as units. In the algebraic symbol, however, we 
have a means of designating any number whatever. 
The symbol c which was used in this problem repre- 
sents a number which is not known until the problem 
is solved. The advantage of this is that we may use 
this symbol as a term in our number manipulation 
without knowing what actual number it represents. 
The symbol represents a definite number so long as the 
other terms used in the problem are defined, but if we 
take an algebraic formula in which all of the symbols 
are of the indefinite algebraic sort, then the formula 
will hold true whatever definite numbers are substi- 
tuted for the algebraic symbols. If certain of them 
have numbers substituted for them, this restricts the 
possibilities for the others. The only requirement then 
is that the same symbol be represented by the same 
number throughout the solution of the problem. 

Arithmetical sjrmbols may represent indefinite 
quantities, but in a roundabout way. It will be well to 
clear up a question which may occur with reference to 
the statement which has just been made. One may ask 
how it is that, if the arithmetical symbols — that is, 
the digits or numbers made up of them — can repre- 
sent only specific numbers, and the algebraic symbols 
alone can enable one to solve problems in a different 
way because they represent unknown numbers, or 
may represent a variety of definite numbers, the above 
problem can be solved by arithmetical means. In 



MATHEMATICS 2lS 

order to answer this question, we must qualify the 
statement that the arithmetical symbols represent 
only definite numbers. We have already seen in the 
previous discussion of arithmetic that a combination 
of numbers in the fraction, representing a ratio, may 
represent a more abstract relationship than is repre- 
sented by a single number. Three quarters represents 
nine when the total group which is thought of is 
twelve, but it represents twenty-four when the total 
group is thirty-two, and seventy-five when the total 
group is one hundred. The use of percentage as a form 
of application of ratio enables one to use the symbol 
which may have a variety of definite numerical quan- 
tities. In the case before us the cost was represented 
by 100 per cent, that is, by the ratio {U and the 
profit by 12| per cent, or i^j. These ratios, then, are 
of the same nature as the algebraic symbol c. The 
difference is that the unknown quantity may be more 
conveniently represented by a symbol which does not 
imply any definite number than by a ratio which is 
itself made up of two definite numbers. It is more 
easily grasped as a symbol which represents an un- 
known quantity than is the numerical ratio. It is 
true that both methods may be pursued in such a case 
as this, but in the more compUcated forms of opera- 
tion, the use of symbols which evidently represent an 
unknown quantity is easier and better understood. 

Manipulation of the equation is a central element in 
algebraic procedure. The above problem illustrates 



214 PSYCHOLOGY OF COMMON BRANCHES 

also another fundamental fact in regard to algebraic 
processes. After the algebraic symbol had been intro- 
duced, the problem was stated in the form of an equal- 
ity between two quantities, one of which contained 
the symbol for the unknown quantity. This statement 
of an equality is the equation, and the equation, with 
the rules and the principles for manipulating it, is one 
of the most fundamental elements in the algebraic 
form of procedure. 

The equation merely states the result in arithmetic, 
but is used to obtain the result in algebra. The equa- 
tion is implied from the very beginning of the study 
of arithmetic. When the child realizes that three 
groups of four each are equivalent to a group of twelve, 
he is recognizing an equality between two forms of 
grouping, and may state the equality in the form of an 
equation. In arithmetic, however, the operations are 
all performed on one side of the equation and the 
equation is used merely to state the result of these 
operations. Take a more complicated form of multi- 
plication, such as 24 times 30. In this case the multi- 
plication of the two numbers is carried on as a series 
of processes and then the result is stated in the form, 
24 X 30 = 720. The equation only expresses the re- 
sult of the multiplication which has been carried on 
with the terms on one side of the equation. In algebra, 
on the other hand, the problem is stated first in the 
form of an equation, and the solution is reached by 
manipulating the terms or the symbols not merely on 



MATHEMATICS 215 

one side, but on both sides, or by adding, subtracting, 
or performing other operations alike with both sides. 

An illustration of the use of the equation in algebra. 
Here again we may make the matter clearer by illus- 
tration. Take as a problem one of Sam Lloyd's puz- 
zles. The following problem serves the purpose: " At 
a certain time between seven and eight o'clock, the 
two hands of a clock are at equal distance from the 
mid-point of the dial at the bottom, that is, from the 
point that represents the half-hour. At what time are 
the hands in such a position? " 

The conditions of the problem must first be put into 
algebraic symbols. It is obvious that we have here a 
complicated set of conditions which are difficult to 
express or to work out by using only the definite quan- 
titative symbols of arithmetic. Suppose, then, that 
we use a symbol to represent one of the unknown 
quantities, which, if it were known, would enable us 
to answer the problem. Let a;, this unknown symbol, 
represent the number of minutes past the hour which 
the minute-hand has progressed, or in more general 
terms the number of minutes past the hour which is 
represented by each of the two hands. We may now 
make up an equation from these assumptions. The 
position of the minute-hand to the right of the bottom 
or the mid-point of the dial will be represented by the 
difference between thirty minutes and the minutes 
past the hour which the hand indicates; that is, the 
position will be represented by 30 — x. This distance 



216 PSYCHOLOGY OF COMMON BRANCHES 

is equal, according to the conditions of the problem, 
to the distance from the bottom mid-point to the 
hom*-hand. This distance we can also represent by 
means of our symbols. Since the hour-hand progresses 
through a distance representing five minutes on the 
dial, in the same time that the minute-hand progresses 
throughout a distance representing sixty minutes, and 
since they progress at a proportional rate of speed, 
the distance which the hour-hand has traveled from 
the seven o'clock point toward the eight o'clock point 
will have the same ratio to five minutes that the dis- 
tance the minute-hand has to travel has to sixty min- 
utes. Since the distance the minute-hand has traveled 
is represented by x, the distance which the hour-hand 
has traveled is represented by 

1 J. X 

—z ot X, or — -. 
12 12 

The position of the hour-hand beyond the bottom 
mid-point, then, is 5 +— , since it started at the begin- 

ning of the hour at a point five minutes beyond the 
thirty-minute point. According to the conditions of 
our problem, these distances are equal, and we may 
state the problem in mathematical terms as follows: — 

30-a;=5 + :^. 
12 

The equation must then be solved. So far the prob- 
lem has been merely to put into algebraic terms the 
statement of the question. The rest of the solution of 
the problem consists in so manipulating the equation 



MATHEMATICS 217 

which we have stated that the value of x will be found. 
The operations are represented according to the 
familiar manner, as follows: Transposing the 5 and 
the X so that the numerical quantities are on the same 
side and the values of x are together, we get as a result 

Then x = ^ X 25, or 23iV. 

If we apply this value of x to our problem, we find 
that the distance which the minute-hand is from the 
thirty-minute point is 30— 23iV, or 6H, and that the 

23tV 
hour-hand is distant from this same point — -r- + 5, or 

12 

the same number, 6H. The process which is involved 
here, besides setting the problem into algebraic terms, 
is the solution of the problem by manipulating the 
equation. This latter part of the solution necessitates 
learning the principles which govern what can be done 
with an equation. In general, these may be summed 
up by saying that what is done to one side of the equa- 
tion must also be done to the other. This principle, 
of course, works out into many detailed forms of pro- 
cedure, but it is one of the fundamental principles of 
algebraic work. . 

Algebraic expressions may be made concrete by 
substituting numerical quantities for the symbols. 
When an algebraic operation, which is represented 
by the algebraic symbols and their manipulations, be- 
comes obscure, the matter may be cleared up and the 



218 PSYCHOLOGY OF COMMON BRANCHES 

terms made more concrete by the substitution of 
numerical quantities for the symbols. This is, in prin- 
ciple, the same sort of process that is carried on when 
we substitute concrete objects for numbers in early 
number work, — as when the child uses splints or 
marbles, or measures areas or lengths, in order to illus- 
trate or make concrete the meaning of numbers and 
of their combinations. In the same way we approach 
the concrete in algebra when we substitute definite 
numbers for the algebraic symbols. 

Negative numbers require an intricate mode of 
representation. Some of the notions which are em- 
ployed in algebra may be represented concretely, 
though by somewhat intricate devices. One of these 
is the idea of negative numbers. If we substitute 
numerical quantities for negative algebraic symbols, 
we cannot manipulate them in the same way in which 
we do positive numerical quantities, and we cannot 
illustrate their meanings in the same simple way by 
substituting concrete objects. In order to grasp the 
meaning of negative numbers and of the operations 
which are made with them, it is necessary to use some- 
what more complex spatial relations and to illustrate 
by a combination of these relations and of movements 
through space. 

Addition and subtraction may be illustrated by dis- 
tances on a line from a middle point. To represent 
positive and negative quantities for the purpose of 
addition and subtraction is fairly simple. All we have 



MATHEMATICS 219 

to do is to use a straight line with a dividing point in 
the middle, and represent positive quantities by dis- 
tances toward the right and negative numbers by dis- 
tances toward the left. If we have to add a positive 
and a positive number, we merely add the correspond- 
ing distances in the same direction and we arrive at a 
result which is equal to the sum of the two numbers. 
The addition of a positive and a negative number is 
represented by a distance toward the right and then a 



«-H — I— I — I — I — I— J — I — I — I — I — I — I — ►— I — I — i-^ — t— 4 



.-2 



}+4+(-2) 
^1+6- (-3) 



FlQ. 11. CONCRETE REPRESENTATION OF OPERATIONS 
WITH NEGATIVE NUMBERS 

distance from this point to the left, each corresponding 
to the size of the number. (See Figure 11.) The opera- 
tion then is performed by subtracting the negative 
number from the positive, or the positive from the 
negative, and aflSxing the sign of the larger number. 
The subtraction of one number from another can be 
represented by movements in the direction opposite 
from that indicated by the sign of each number. 
Thus, if we subtract a negative from a positive num- 
ber, it is the equivalent of adding two positive num- 
bers. 

In the case of multiplication we must resort to a still 



220 PSYCHOLOGY OF COMMON BRANCHES 

more complex form of concrete representation. Mul- 
tiplication of negative numbers may be illustrated by 
the accompanying Figure 12, adapted from Myers's 
First Year Mathematics. The line AB may be taken 
to represent a bar which turns about a fulcrum in the 
center. The distances along this bar toward the right 




FlO. 12. CONCRETE REPRESENTATION OF OPER- 
ATIONS WITH NEGATIVE NUMBERS 

are represented by positive, and along the left by 
negative, numbers, as in the case of addition and sub- 
traction of negative numbers. A force acting upward 
upon this bar represents a positive number and a force 
acting downward, a negative number. The two num- 
bers which are to be multiplied are represented, one 
by a position upon this bar to the right or the left of 



MATHEMATICS 221 

this fulcrum, and the second by a force acting upon it. 
The result is represented by the turning of the bar, 
and when this is in a direction opposite to the move- 
ments of the hands of the clock, it is designated as 
positive, and when it is in the direction the same as the 
movement of the hands of the clock, it is designated as 
negative number. The sign of the product may then 
always be found by representing one of the numbers 
which is to be multiplied by a position on the bar 
corresponding to its sign, the other number acting in 
the direction corresponding to its sign, the sign of the 
result corresponding to the movement produced on 
the bar. Thus a positive number multiplied by a 
positive, represented by an upward force acting upon 
the right side, always results in a positive result or 
multiplicand. Similarly, a negative number multi- 
plied by a negative results in the same way. On the 
other hand, a negative number multiplied by a posi- 
tive always results in a movement in the negative 
direction. 

These illustrations make clear the abstractness and 
complexity of algebra. It is evident that we are here 
getting into an abstract matter, since we represent 
the mathematical relationship by such a combination 
of directions, distances, movements, and resultant 
movements. These may serve as examples of some of 
the more important of the ideas which are developed 
in algebra. They go beyond the arithmetical proc- 
esses; and in virtue of this fact, they make it possible 



222 PSYCHOLOGY OF COMMON BRANCHES 

to handle number relations in a way that is not possi- 
ble in using the more definite and less manageable 
number symbols. Algebra is both a more complex and 
a more valuable tool than is arithmetic and requires 
for its mastery a higher degree of abstractness and p 
higher type of intellectual process. 

The development of geometry from measurement 

In the discussion of number and its development in 
arithmetic and algebra we saw that the various rela- 
tions of numbers may be illustrated by means of 
measurements of lengths, areas, or volumes; and that 
these may be used as illustrations of the relationships 
between numbers and the various number operations, 
such as addition, multiplication, etc. From that point 
we have traced the lines along which the development 
of number has been specialized. We have met more 
and more complicated ways in which numbers may 
be dealt with in the various operations of arithmetic, 
and have seen how, by the use of more abstract sym- 
bols, the more general operations of algebra are possi- 
ble. The early form of measurement which is used to 
illustrate number is developed in another direction by 
giving particular attention to the relations of forms 
and spaces and distances, and to the general principles 
which govern them. The development of the princi- 
ples governing the spatial relations is called "geom- 
etry." The relations of geometry to measurement 
may be seen from the word itself. In its origin, the 



MATHEMATICS 223 

word meant the measurement of the earth, and, in 
conformity to this meaning, geometry was developed 
out of measurement of land for practical purposes. 

In the school and in the history of the branch there 
is a distinction between measurement and formal 
geometry. In the school curriculum there has been a 
sharp division between the early measurement which 
the child carries on and which may be used to represent 
the number processes and the later refinement of these 
same studies of spatial relations as it appears in the 
form of EucUdian geometry. The distance or gap 
which separates the early or crude measurements from 
the formal study of the principles of the relations of 
space is one which has resulted from the fact that our 
geometry is inherited from the Greek philosopher 
Euclid. Geoemtry in the English schools has always 
been called by the name of Euclid, who first system- 
atized the principles of the subject. Many of these 
principles were known in a concrete way before 
Euclid. Many of the general propositions of Euclid 
were discovered by practical experimentation, and 
were practically applied, before Euclid worked out 
their proof and formulated his principles. The Egyp- 
tians understood the relations between the diameter 
and the circumference of a circle and between the 
hypothenuse and the legs of a right-angled triangle, 
but they had not worked out the formal demonstra- 
tion of these relationships. 

Accurate measurement may give the child an early 



224 PSYCHOLOGY OF COMMON BRANCHES 

knowledge of many geometrical principles. These 
historical facts suggest that many of the facts regard- 
ing space may readily be learned by the child before 
he undertakes the study of their rigid proof. The gap 
between the early crude measurements, which are 
connected with the first appreciation of numbers, and 
the formal study of geometry might then very well be 
filled in by a somewhat more exact use of measurement 
through which the general principles of the spatial 
relation could be experimentally discovered. This 
would prepare the child who is to go on to the formal 
study of geometry by giving him a better concrete 
basis for his more abstract study of principles, and it 
would furnish to the child who is not to go on the direct 
knowledge of spatial relations which would be of 
value to him. 

Many geometrical generalizations may be worked 
out concretely before the child can understand their 
demonstration. That geometry has been placed later 
than algebra in the high-school curriculum is due to 
the fact that the extremely abstract form of geom- 
etry, or the study of space, has been used to the exclu- 
sion of the more concrete study of the same facts. If 
geometry is studied through measurement, it may be 
considerably more concrete than algebra or even some 
of the topics of arithmetic. Thus, a pupil may gain a 
practical appreciation of the fact that the area of 
a rectangle is measured by the product of the length 
of the two adjacent sides, or even of the fact that the 



MATHEMATICS 225 

square on the hypothenuse of a right-angled triangle 
is equal to the sum of the squares on the two legs, 
without going through any rigid demonstration of 
these facts. Thus the child will come to recognize cer- 
tain geometrical facts in the same way that he learns 
to make other generalizations. This procedure consists 
in recognizing that a fact holds true in a number of 
cases, and in the conclusion that it is true in general. 
Take the first illustration which was used. If the 
child has measured a large number of rectangles, and 
finds that the squares which are made by drawing 
lines at unit distances to connect the opposite sides 
are equal in number to the product of the unit dis- 
tances on the adjacent sides, he will arrive at a general- 
ization that this is always true of rectangles. There is 
no reason why he might not properly make this gen- 
eralization before he has learned its rigid proof. We 
do not wait to teach the child generalizations in nat- 
ural science, until he is able to appreciate their sci- 
entific demonstration. 

The Pythagorean Theorem may be illustrated con- 
cretely. Take two illustrations of the appreciation of 
spatial relations of a fairly complex sort through the 
method of measurement, or of direct apprehension, 
rather than through demonstration. The Pythagorean 
Theorem serves as a good example. In Figure 13 we 
have a special case of the theorem. It may be illus- 
trated for the child by having him construct a right- 
angled triangle with one leg four units long and the 



226 PSYCHOLOGY OF COMMON BRANCHES 

other three units long, and then having him construct 
the squares upon the three sides. He will find that the 
hypothenuse measures five units long, and then, if he 
divides each of the squares into smaller squares of 




Fig. 13. ILLUSTRATION OF THE SOLUTION OF 
THE PYTHAGOREAN THEOREM BY MEASURE- 
MENT 

unit length on each side, he will find that the two legs 
are measured by squares of sixteen and nine units, 
and the hypothenuse by a square of twenty-five units. 
Thus he can see that in this particular case the square 
upon the hypothenuse is equal to the squares upon 
the two legs. 

A more general mode of representation may also be 
used. A similar relation for right-angled triangles in 



MATHEMATICS 



227 



general may be well illustrated by Figure 14, which is 
a little more complex and suited to a more advanced 
stage. ABC is a right-angled triangle and ABKD is a 
square constructed 
on the hypothe- 
nuse. ACEF and 
BCHG are squares 
constructed on the 
two legs. Let the 
child connect D 
and F, extend CE 
and drop the per- 
pendiculars KJand 
KI. He may then 
determine by meas- 
urement or by su- 
perposition that 
KJEI and BCHG 
are equal. There- 
fore, the irregular 
figure KJFACI 
represents the squares on the two legs. If this figure 
can be shown to be equivalent to ABKD, the gen- 
eral truth of the theorem is evident. This can be 
done by superimposing ABC on AFD and BIK on 
KDJ. 

This generalization is to be distinguished from 
rigid proof. In the stage that we are supposing, the 
child is not expected to prove the equivalence of the 




FlO. 14. ILLUSTRATION OF THE SOLU- 
TION OF THE PYTHAGOREAN THEOREM 
BY MEASUREMENT 



228 PSYCHOLOGY OF COMMON BRANCHES 

two figures. He may, however, see that they are 
equivalent by measuring the various parts as indi- 
cated, provided that the figure has been constructed 
with sufficient care so that it is accurate. The proof 
of such a conclusion as this requires much more than 
the demonstration that it is true in one particular 
figure. The child may recognize its truth and may 
generalize upon this so as to conclude that it is true 
for all figures of certain specifications; but to prove 
that it must be true for every figure which meets these 
specifications is a different matter. 

Rigid proof bases conclusions on assumed axioms 
or on previously proved conclusions. An advance to 
the geometry of proof depends on the appreciation of 
logical requirements. The final stage of development 
in geometry, then, is not merely the recognition that a 
certain relation holds true, but rather the appreciation 
of the answer to the question why this relation must 
be true. The very obviousness of the fact that a fact 
is true is frequently the greatest source of difficulty to 
the pupil in determining why it must be true. To raise 
a question that the shortest distance from a point to 
a straight line is a perpendicular seems a foolish thing 
to do, and this is true also of many other geometrical 
theorems. The pupil is not ready for this demonstra- 
tional type of geometry until he can appreciate the 
requirements of a logical series of steps, each of which 
depends upon some assumption which is either an 
axiom or a previously demonstrated theorem. 



MATHEMATICS 229 

Geometry proceeds from concrete to abstract as do 
arithmetic and algebra. When the form of proof has 
been gone through in this manner, it becomes a general 
or abstract affair which does not rest merely upon the 
appreciation of a relation in a certain concrete figure. 
In geometry, as in arithmetic and algebra, we begin 
with the understanding of certain concrete relations, 
or relations among concrete objects, and then gradu- 
ally progress until the relations can be understood 
abstractly. When this stage is reached, the pupil uses 
a concrete figure only as an illustration or a mode of 
representing the conditions of the problem to his mind. 
The proof of this problem rests upon the appreciation 
of the dependence of the theorem upon a series of 
previously demonstrated theorems. 

An illustration of the discovery of a geometrical 
proof. The following illustration may serve to show 
how one proceeds in geometrical proof. Suppose that 
we set out to prove that a straight line which is per- 
pendicular to each of two intersecting straight lines 
at their point of intersection is perpendicular to the 
plane P of these lines. This means that the line must 
be proved to be perpendicular to any other straight 
line whatever of the plane P which intersects at the 
same point. In Figure 15, assume the line AO perpen- 
dicular to OB and OC in the plane P. To prove that 
the line AO is perpendicular to any other straight line 
in the plane drawn through the point 0, as OD. 

The conditions of the problem are first clearly real- 



230 PSYCHOLOGY OF COMMON BRANCHES 



ized. The pupil first attempts to get clearly into mind 
what the conditions of the problem are, and then to 
cast about for methods of proving, on the basis of the 

conditions which 
are known, that 
which is to be 
proved. We know 
that ^OC and ^05 
are right angles, and 
we wish to prove 
that AOD is a right 
angle. One method 
with which the stu- 
dent has already 
become familiar is 
the use of triangles. 
One may construct 
a number of trian- 
gles by drawing the 
lines ABy AC, and 
CB, then another 
triangle may be 
constructed, or a series of triangles, by connecting A 
with the point of intersection of OD and BC at D by 
the line AD. 

The student follows up promising clues. This, how- 
ever, does not seem to lead directly to the proof. An- 
other form of procedure which is commonly used is 
to extend a line, such as AO, through the plane to an 




MATHEMATICS 231 

equal distance on the other side, represented at E. 
By connecting B, C and D with E, we have another 
series of triangles. It is obvious that if the triangle 
AOD can be proved to be equal to EOD, the angles 
AOD and EOD will be proved to be right angles. A 
number of triangles are easily proved to be equal, as 
AOC and EOC, and AOB and EOB. This suggests 
that the triangles ABC and EBC may be shown to be 
equal, because the three sides are equal, and that by 
this means the triangles ADC and EDC can be proved 
to be equal. As a consequence AD and ED are equal. 
This makes it possible to prove the equality of AOD 
and EOD, and therefore of the angles AOD and EOD, 
and proves that they are right angles. 

The process of problem-solving is usually more ran- 
dom. The student in solving this problem would com- 
monly not have arrived at the steps in such a direct 
manner. A great many more useless ideas would have 
been considered and rejected before the series of steps 
which led to the final solution was finally hit upon. 
The degree of directness with which the student pro- 
ceeds to the conclusion depends somewhat on the 
amount of his previous experience in solving such 
problems, and upon his familiarity with the various 
possible methods of approach. 



232 PSYCHOLOGY OF COMMON BRANCHES 

Problem-solving 

Problems are solved by analyzing conditions pre- 
sented and following up clues. The procedure which 
is taken in solving such problems illustrates the gen- 
eral method of attacking such problems, and fur- 
ther illustrates the method of problem-solving or of 
reasoning in general. We may very briefly summa- 
rize the characteristics of such procedure. In the first 
place, one starts out with a problem, which may be 
in the form of a certain conclusion which is to be 
tested. With this problem in mind, the conditions are 
analyzed, or broken up, in order that one may get a 
clear realization of the various elements of the prob- 
lem. One then casts about in his mind for various 
clues to the way in which the solution may be ap- 
proached. In this he is aided by methods which have 
been found to be suitable in similar cases in the past. 
The methods which are suggested are then tried out 
until one is found which leads to the appropriate series 
of steps and finally to the conclusion. These steps 
must be so connected that each following one de- 
pends upon the one preceding. 

Solving a problem is radically different from fol- 
lowing the statement of a completed proof. The means 
by which the steps in a solution are stated after the 
solution has been reached must not be confused with 
the steps through which one goes in reaching the con- 
clusion. The identification of these two is responsible 



MATHEMATICS 233 

for the fact that many students of geometry never 
learn to attack the problems themselves. The demon- 
strations are stated by building up the proof in a logi- 
cal manner, step by step, by beginning with known 
facts and proceeding in an orderly way to the conclu- 
sion. The proof is reached by the student, however, 
by beginning with the conclusion which is to be proved 
and working back to the facts which may serve as the 
basis for such a proof. In a measure the two processes 
begin at opposite ends, and one should distinguish 
them in mind as well as in practice. 

Problem-solving appears most prominently in geom- 
etry. This consideration of problem-solving in geom- 
etry leads us to the question of problem-solving in 
number work in general. Problem-solving is a some- 
what more intimate part of the work in geometry than 
of arithmetic and algebra, because of the fact that 
each new theorem is a new problem in itself and is a 
step in a whole series of problems which are closely 
knit together. In the case of arithmetic and algebra, 
the particular problems which the child is set to solve 
are grouped about certain general types of solutions. 
The pupil is led to apply a certain method of solution 
to a large number of concrete situations. In this proc- 
ess he is not developing a new proof or the proof of a 
new fact, but is applying to a variety of situations a 
method which he has learned to use. 

The grasp of the statement of the problem is im- 
portant in arithmetic and algebra. Although there is 



234 PSYCHOLOGY OF COMMON BRANCHES 

this difference in problem-solving in geometry and in 
the other branches of mathematics, yet the general 
features of the mental process are the same in the dif- 
ferent fields. In the case of arithmetic and algebra, 
however, we meet with a phase of the matter which is 
prominent in them and which is one of the important 
conditions which govern the ability to solve prob- 
lems. It has been found by experiment that the diflS- 
culty in solving an arithmetic or an algebra problem 
depends in a large measure upon the ability of the 
pupil to understand what the statement of the problem 
means. Courtis found as reported in Bulletin num- 
ber 2 of the Courtis Standard Tests, August, 1913, that 
the same problem could be stated in a variety of ways, 
and that the success of the pupil in solving a problem 
varied remarkably with the variation in the manner of 
stating it. There is a distinction between the appreci- 
ation of a mathematical relationship, or a method of 
manipulating mathematical symbols to obtain certain 
mathematical results, and the ability to apply these 
mathematical processes to a practical concrete prob- 
lem. One may understand the mathematics itself very 
well and yet not know what process to choose to solve 
a special concrete problem. 

Understanding a problem usually involves a clear 
grasp of concrete objects and relationships. The first 
step in solving a mathematical problem is the under- 
standing of what it means in its concrete terms. The 
failure to reach this understanding is seen sometimes 



MATHEMATICS 235 

not merely in problems in arithmetic and in algebra, 
but also in geometry. The student of geometry, par- 
ticularly of solid geometry, sometimes fails to realize 
that the lines which are used to represent the figures 
represent spatial relations. Until a student can get a 
clear grasp of the sort of figures which are intended, he 
is not in a position to understand in any measure the 
problem or its demonstration. In the case of problems 
in arithmetic or in algebra, the first requirement is that 
the pupil shall be able to picture to himself just what 
the meaning of the problem is. This very frequently 
means the ability to form an image of certain concrete 
objects. Whether such an image is absolutely essential 
or not, it is very likely that it is in all cases beneficial, 
and that the clearness of grasp which is attained by 
the pupil will depend upon the clearness with which he 
can picture to himself the concrete setting of the prob- 
lem. Take the familiar problem concerning the rate 
with which a tank would be filled if water flowed in 
through a pipe of a certain size and out through a pipe 
of another size. The ability to picture the conditions 
of this problem will make it easy for the pupil to know 
what sort of formula to use in its solution, or at least 
will prepare the ground for the knowledge of the math- 
ematical form of procedure which should be used. 

The significance of the mathematical procedure 
must be clearly understood. The next step is obviously 
to turn the problem into mathematical terms or to 
know what form of mathematical solution ought to be 



236 PSYCHOLOGY OF COMMON BRANCHES 

used in a particular case. This means that the pupil 
should grasp not merely the meaning of the problem 
as it is stated, but also the meaning of the various 
forms of solution which he has learned. It frequently 
happens that pupils are able to solve problems which 
are classified under the form of procedure which is 
appropriate for them, but are not able to solve similar 
problems when they are arranged in miscellaneous 
order so that there is nothing to indicate which mathe- 
matical formula is to be used. When a pupil shows a 
great difference between his ability to solve the classi- 
fied and unclassified problems, the probability is that 
the problems have not been real to him, either be- 
cause he did not appreciate their meaning, or because 
he did not understand the meaning of the mathemati- 
cal formulae used. In either case his solution of the 
problems is merely a matter of mechanical juggling of 
terms without an understanding of their use and is 
of no value to him from the standpoint of intellectual 
development. 

Much practice in discovering the general mode of 
solution of problems is desirable. It is well for the 
pupil to have a large amount of practice in the under- 
standing of problems in their concrete statements and 
in determining what form of solution should be used 
for them. This can be done by arranging series of 
statements of problems and requiring the pupil not to 
work them out in detail, but to put their meaning in 
other words and to state how one should proceed in 



MATHEMATICS 237 

general to solve them. By this method the pupil will 
learn to distinguish and understand the general fea- 
tures of the various methods of procedure because he is 
not confused with a mass of details. 

Number illustrates the higher thought processes. It 
has become evident, from this whole discussion of 
number and mathematics in general, how mathematics 
constitutes a form of thought which is not a direct 
reaction to the concrete things of the physical world, 
but rather consists in the development of complex 
systems of thought processes which enable one to deal 
with the concrete processes in an indirect manner. 
One first selects from the multifarious attributes of 
things the number aspect; and then develops forms of 
procedure with numbers wholly or largely abstracted 
from the concrete objects themselves; and finally 
applies the results of these operations to the concrete 
things. Instead of constituting an immediate reaction 
to the physical object, such a response is made up of 
a series of thought processes which are carried on for 
a time with little reference to the objective world. 
The next chapter will be a further illustration of this 
higher form of response. 

REFERENCES 

1. S. A. Courtis: "Standard Scores in Arithmetic." Elementary 
School Teacher (1911), vol. 12, pp. 127-37. 

2. Frank N. Freeman: "Grouped Objects as a Concrete Basis for 
the Number Idea." Elementary School Teacher (1912), vol. 12, 
pp. 306-14. 

3. C. H. Judd: Genetic Psychology for Teachers, chap. 9. Appleton, 
1903. 



238 PSYCHOLOGY OF COMMON BRANCHES 

4. J. A. McClellan and J. Dewey: Psychology oj Number. Apple- 
ton, 1895. 

5. W. S. Monroe: "Warren Colburn on the Teaching of Arith- 
metic." Elementary School Teacher (1912), vol. 12, pp. 4G3-80. 

6. D. E. Smith: The Teaching of Arithmetic. Teachers College, 
Columbia University, 1909. 

7. H. Spencer: Education, chap. 2. Appleton, 1861. 

8. J. W. A. Young: The Teaching of Mathematics. Longmans, 
1907. 



CHAPTER X 

NATURAL SCIENCE: GENERALIZATION UPON 
EXPERIENCE 

Summary. We have seen how the child makes vari- 
ous kinds of responses to the experiences which are 
furnished him by the stimuh from the external world. 
He has to begin with a variety of native responses 
called "instincts." He adds to these or builds upon 
them a great variety of responses which are not in- 
stinctive. One type of response is the response of 
movement to stimulus, and we call the mode of learn- 
ing by which these responses are formed "sensori- 
motor learning." In other cases it becomes necessary 
to organize the stimulus itself so that one comes to 
recognize it as having a meaning and becomes able to 
distinguish the meaning among the different objects 
which he finds it necessary to respond to. Not only 
does the child learn to respond by giving interpretation 
to objects, but he is able to retain impressions made 
upon him so that he may recall them at some future 
time and take them into account in making his re- 
sponses. He is also able to present to himself, in his 
imagination, events or objects which are distant in 
time or space. The child is also capable of responding 
to certain abstract features of the surrounding world 



240 PSYCHOLOGY OF COMMON BRANCHES 

and can build up systems of thought by considering 
these elements. This abstraction is illustrated by 
number. 

Natural science deals with generalizations. In the 
study of natural science we find still another mode of 
dealing with experience. This consists of developing 
ideas or modes of response which are equally applicable 
to a variety of objects or experiences. Take an illustra- 
tion from the very early experience of the child. In his 
early dealings with the physical objects about him the 
child has not yet learned the common laws which 
govern them. He has to learn by experience such a 
fundamental fact as that an object when released falls 
to the ground. After he has seen this happen with one 
object after another, he learns how to prevent objects 
from falling and acquires the habit of expecting to see 
objects fall when they are released. He appears to 
pass through a period when he becomes conscious of 
this general mode of action of things, and delights in 
dropping objects partly for the pleasure in experienc- 
ing the fulfillment of his expectations. Such an idea, 
which applies equally to a whole class of objects, we 
call a " generalization." ^ 

A child's fear of a balloon is explained by the fact 
that it violates his expectation. A good illustration of 
this expectation in the mind of the child, that objects 

• A generalization is an idea which is the outgrowth of a mode of 
response which is found appHcable to a whole class of objects. It is 
usually embodied in the statement of a general principle. 



NATURAL SCIENCE 241 

will fall when released, may be seen in the fear which a 
child exhibited when he saw a toy balloon, which did 
not act in the expected way. Here is an object, which 
according to all previous experiences ought to fall when 
it is released, but instead of that it rises in the air. 
The child who was the subject of this observation was 
very much frightened by this experience, and it required 
some time for him to become accustomed to the un- 
familiar action of the balloon and to enjoy playing with 
it. The child acquires an expectation that things will 
act according to certain regular modes of action or 
laws. He finds that in the world about him certain 
regular kinds of action can be expected. In the early 
stages he develops these expectations unconsciously, 
but this forms the basis for the development of more 
conscious generalizations later on. 

Concept formation 

The child forms concepts, or ideas of classes of 
objects; and general principles, or ideas of the charac- 
teristics or modes of action of these classes. The 
child's generalization upon his experience proceeds in 
two ways. In the first place, he learns to distinguish 
those classes or groups of things which have a certain 
common mode of action or which have something sim- 
ilar, as a result of which one is led to put them into a 
class. The second procedure is to examine in more 
detail the characteristics or modes of action of objects 
which have been classed together. To illustrate these 



242 PSYCHOLOGY OF COMMON BRANCHES 

two processes, the child may exhibit an interest in 
distinguishing between cats and dogs, horses and 
cows, etc., and in learning to recognize the members of 
the different groups; or he may become more interested 
in learning about the habits or characteristics of the 
cat or the dog or the horse. For example, he learns to 
distinguish between cats and dogs by certain marks of 
difference, and by further experience to learn more 
about the particular habits of cats — that they meow 
and scratch, and of dogs — that they bark and bite. 
We may distinguish these two by naming the first 
"concept formation," or the formation of general 
ideas; and the second, the formation of general princi- 
ples or laws. It is evident from the illustration that 
there is not a sharp distinction between the two 
processes. 

The child early classifies objects according to their 
use. The earhest form of a child's scientific develop- 
ment consists in learning to class objects together 
which have common characteristics. The basis on 
which a child first learns to group objects, and to re- 
gard them as belonging to a common class, is their use. 
If a child below nine years of age is asked to tell the 
meaning of common objects with which he is familiar, 
he gives the definition in terms of their use. He will 
say that a fork is to eat with, a chair to sit upon, a 
table is to set things on, a horse to pull a carriage, and 
so on. What a thing can be used for and what it does 
is the characteristic which attracts the child and which 



NATURAL SCIENCE 243 

leads him to put an object into one class rather than 
into another. 

The development of concepts is hastened by the 
use of names. A child begins to classify things roughly 
before he can talk. The infant early distinguishes be- 
tween things as good to eat or good to play with, and 
distinguishes between his own family and others, and 
between those within his own family. The use of names 
greatly facilitates this form of development and leads 
to a finer distinction between things. When a child 
finds a name given to an object, this immediately 
directs his attention to that feature of the object which 
it has in common with other things which are given the 
same name. He would probably be much slower in 
making distinctions and comparisons if he were left 
merely to his own observation in the matter. 

The mistaken application of names illustrates how 
they operate. The kind of mental process to which the 
child is led by the use of names is illustrated in cases 
where he makes a mistake in the application of a name. 
It is related by Preyer that a little boy had been accus- 
tomed to hear his grandmother given the familiar 
name. There was no means of knowing what he 
thought it was which led this name to be applied to 
his grandmother, until one day he saw another old 
lady who also wore a cap. He thereupon called her 
"grandmother" also, thinking apparently that a 
grandmother was a person who wore a cap. This illus- 
trates the fact that he had, without thinking particu- 



244 PSYCHOLOGY OF COMMON BRANCHES 

larly about it, selected a certain feature to which he 
thought the name appHed, and when he saw another 
who possessed the same characteristic, he extended 
the name to her also. 

Mistakes emphasize the importance of selecting the 
essential feature as a basis for classifying objects 
together. Another illustration shows how a child may 
group a great many diverse things together by select- 
ing in each case some feature which is common to two 
things and thus finally reaching in his chain of thinking 
an object which is widely different from the one with 
which he started. A little boy saw a duck upon a pond 
and heard the word " quack " applied to the duck. 
He did not clearly separate in his mind the duck and 
the water and so applied the name to both. Later he 
used " quack " to refer to water or even to any liquid. 
Further, he applied the name to other birds than the 
duck, then to an image of an eagle upon a coin, and 
finally to coins themselves. We see how far this 
process of association may carry the child from the 
original object to which the name was given. These 
cases of accidental or erroneous association emphasize 
the opportunity and need for the direction of the child's 
thinking in the formation of his concepts or general 
ideas. They bring out also the fact that a concept is 
built upon the analysis of an object so as to determine 
what the essential feature is. It is necessary, in order 
that the child may have the correct notion, that he 
should select the essential feature and not some acci- 



NATURAL SCIENCE 245 

dental feature upon which to base his classification of 
the object. This thought process in selecting the cor- 
rect feature is of considerable value, and names, there- 
fore, may form a stimulus to valuable thinking on the 
part of the child. 

The development of generalization 

The child's early explanations are superficial. It 
may thus be seen that the process of grouping things 
together goes parallel with the process of familiarity 
with the characteristics of the things themselves. The 
more one knows about individual objects, the better 
he is able to tell to what class they belong, and to 
divide them up into finer and finer groups. In the 
beginning the child shows a disposition to follow the 
practice of primitive man and to depend upon a super- 
ficial similarity in putting things into the same class. 
When he meets with new objects, he shows a disposi- 
tion to think of them after the analogy of things which 
he already knows. In this he is not unlike mankind in 
general, but as he gains in intellectual growth he is 
able to distinguish the characteristics of new things 
which make them fundamentally different from objects 
which he has met before. This tendency to interpret 
new things after the analogy of familiar things is 
shown in the story of the Indians, who, when they 
first saw a steam engine, were greatly puzzled until 
they explained the running of the machine by saying 
that there were horses inside. They were oblivious to 



246 PSYCHOLOGY OF COMMON BRANCHES 

the fact that the running of a horse is as mysterious a 
thing as the working of the steam engine, for since 
they were familiar with the horse's activity, it did not 
present this difficulty to them. The difficulty to them 
lay in the unfamiliarity of the new thing rather than 
in an appreciation of the problem which really existed 
in explaining it. 

The child is ready first to learn the more obvious 
and external facts about things. The child's early 
scientific procedure is after the same manner. It con- 
sists in gaining familiarity with the mode of action or 
with the characteristics of a great variety of things, 
without going very deeply into their explanation. 
Animals and plants are particularly suitable for the 
child's early study, both because of his native interest 
in them and in their habits, and because the familiar- 
ity which he gains with them will serve as a basis for 
the later, more penetrating study which he will have 
to make. He is very much interested in learning about 
such facts as the habits of animals. He may be told of 
the nest-building of birds, the differences in the kinds 
of nests built by different birds, the way in which the 
beavers build their homes, the different modes of 
gathering food and caring for the young, and so on. 
These facts should not merely be taught to the child 
through verbal instruction, but he should also be led 
in the early period to begin the habit of observation. 
It is surprising what a fund of information a child may 
gather if he once becomes interested in such a pursuit. 



NATURAL SCIENCE 247 

In a similar manner the child may learn about the 
habits of plants; the different kinds of seeds which are 
produced by different plants; the ways in which seeds 
are carried from one place to another, or are given 
such form that they will readily spread; the other 
means of growth of plants, as from bulbs, seeds, cut- 
tings, etc. He may leam also of the care which is 
necessary for the growth of plants as well as of animals. 

Care for plants and animals stimulates the child's 
interest and gives him moral training. Subjects of 
study of this sort are particularly appropriate for 
another reason. They give the child an opportunity, 
if conducted in the proper manner, of doing something 
with things, as well as learning about them. The child 
may find out about animals and plants by actually 
caring for them. The care of a pet and the cultivation 
of a garden plot greatly stimulate his interest and lead 
him to learn a variety of things in a way in which he 
will not forget. Incidentally the child learns many 
lessons which are not directly related to scientific 
training, such as the lesson of thoughtfulness and sym- 
pathy in caring for animals, and the lessons of indus- 
try and order. 

This simple type of science suits the child until the 
intermediate period. By such experiences as these, 
the child gains a familiarity with the more obvious 
characteristics and habits of natural objects. This 
forms the foundation for his later scientific work, but it 
needs to be carried much farther in order to be fully 



248 PSYCHOLOGY OF COMMON BRANCHES 

developed. The type of observation and learning of 
facts which have been described is suitable to the 
younger child. The child can begin at least in the 
kindergarten period, and carry forward this type of 
work until some time in the intermediate period in 
school life. At this time he is ready to begin a some- 
what more systematic and thorough form of study. 

More systematic study is necessary to get at many 
of the facts of the world about us. Many of the facts 
of the world about us may be gained by such observa- 
tions as the child can make in this early scientific work, 
but the facts must be on the surface and not require 
too much thought or too sustained observation in 
order that they may be discovered. For the discovery 
of many scientific principles, which are commonplace 
with us, the casual observation of mankind has not 
been sufficient. Adults miss many of the generaliza- 
tions which would be very valuable to them and very 
closely related to their welfare if they were discovered, 
and the child is less capable of systematic observation 
and generalization than is the adult. Many illustra- 
tions of the weakness of unscientific observation are 
at hand. The farmer may go on for generations raising 
corn without discovering the best method of improving 
his product, although all the facts which are necessary 
to the discovery of such a method are at hand for his 
observation, and although it is greatly to his interest 
to discover them. A little scientific observation and 
experimentation enables one to discover these princi- 



NATURAL SCIENCE 249 

pies. For a long time man suffered disease and death 
from yellow fever without discovering that it is related 
to the mosquito, although this fact was at hand all the 
time for observation. In many cases also mankind has 
clung to the first generalization, although systematic 
observation would prove their falsehood. This is the 
case with such common superstitions as that a rabbit's 
foot gives good luck, or that Friday and 13 are likely 
to bring bad luck. 

Science is based on systematic observation and 
experimentation. The means to a more scientific and 
reliable form of procedure, leading to better estab- 
lished principles, have been incidentally indicated. 
They consist in a systematic observation of facts 
together with making a record of the results of the 
observations in order that they may be compared; and 
in experimenting in order that various possibilities 
may be tried out and their results compared with one 
another. Both of these methods imply that one starts 
out with a definite problem in mind, and conducts his 
observation or his experimentation in such a way as 
to gain an answer to the problem. One must be able 
to control his investigations and guide them continu- 
ously and systematically toward the solution of a par- 
ticular question. The ability to carry on such scientific 
work is one which develops gradually, and does not 
appear until the child has at least reached the period 
of his intermediate school life. 

Systematic observation leads to generalization con- 



250 PSYCHOLOGY OF COMMON BRANCHES 

ceming the sun's movements. The way in which 
observation and experimentation make generahza- 
tions more exact, and lead to the discovery of relation- 
ships which would otherwise be unnoticed, may be 
illustrated by two concrete cases. The first is an illus- 
tration of more exact generalization through system- 
atic and directed observation. In certain realms we 
cannot carry on experiments because the forces which 
are to be observed or the events which are to be re- 
corded are beyond our control. In astronomy, for 
example, we have to confine ourselves to the observa- 
tions of events as they take place. Thus, a child may 
notice certain general and superficial facts, but may 
require controlled observation to carry his generaliza- 
tions beyond the more rough-and-ready ones. One 
notices without giving especial attention that the sun 
rises in the east and sets in the west, and that it is 
higher in the summer than it is in the winter. To find 
out more exactly the movements of the earth in rela- 
tion to the sun, one may make a systematic study of 
the shadows which are cast by some object. Suppose 
the child marks on the floor the position of the shadow 
of the corner of the window, or of some object upon 
the window, from day to day. If he keeps a record of 
this position, he will notice that it has the same east 
and west position at a particular hour every day, but 
that it shifts north and south with the change of the 
season. This will lead then to a more definite and 
exact statement of the movement of the sun. 



NATURAL SCIENCE 251 

Exact science often requires the use of number. 
Take another problem, — the relationship of the length 
of the shadow to the height of the object which casts it. 
One may readily recognize, without using any exact 
means of measurement, that the taller object casts the 
longer shadow, but the comparison of different objects 
and the shadows which they cast enables one to make 
the generalization that the shadow is exactly propor- 
tional to the height of the object which casts it. This 
illustration shows how the more exact generalizations 
in science require the use of numbers, just as we found 
that the recognition of the longer stretches of time 
necessitates putting time into terms of numbers. This 
is one reason why the more exact and comprehensive 
forms of generalization cannot be made until the 
child has attained a certain degree of mental develop- 
ment. 

In experimentation causes are studied by introduc- 
ing or varying one at a time. Often the facts which are 
needed for the solution of a scientific problem can be 
obtained more quickly by an experiment than by wait- 
ing until they present themselves for observation. An 
experiment also has another advantage, which is that 
the particular fact which we wish to observe can be 
made to appear singly; or at least we can observe the 
effect of certain conditions by varying those condi- 
tions while others remain constant. Suppose that we 
wish to determine what conditions are necessary for 
the best growth of plants. We may, through experi- 



252 PSYCHOLOGY OF COMMON BRANCHES 

ment, try out one condition after another, taking one 
at a time. We may vary the amount of water supply, 
or the amount of air, or the amount of sunhght, or the 
kind and amount of fertihzer with which the plant is 
furnished; and by keeping an exact record of the 
changes which we introduce and of the results which 
follow in the condition and growth of the plant, we 
may gain an exact generalization as to the bearing of 
these different factors. 

Science is based on the attempt to solve problems. 
These illustrations indicate, as has already been re- 
marked, that scientific investigation consists in carry- 
ing on systematic observations and experiments to 
answer certain problems. The importance of this 
problem-solving process for the education of the child, 
particularly in natural science, has been very greatly 
emphasized, and with good reason. If the child merely 
learns by rote those conclusions which have been 
reached by others, he may gather a very large amount 
of information, but he will not be forming those habits 
of thought and action which will enable him the better 
to meet those problems which may confront him in the 
vocational or other situations of his life. The presenta- 
tion of the work in such a way that it will arouse ques- 
tions in the mind of the child and lead him to an inves- 
tigation of these questions is of great importance. 

The discovery of problems is also important. The 
illustrations which have been used and the principles 
which have been indicated bring out also another form 



NATURAL SCIENCE 253 

of scientific work. The ability to do work of a scientific 
character depends not merely upon the capacity for 
working out problems, but also, and perhaps in a still 
more important degree, on the ability to see problems 
where they have not before existed to the mind of 
other observers. The successful scientist, or the suc- 
cessful investigator in any field, is the person who sees 
questions in what the ordinary individual takes as a 
matter of course. This principle is to be applied both 
in the natural sciences or in the sciences in a technical 
sense, and in any field of human endeavor which ad- 
mits of study by scientific methods. It applies to the 
problems of everyday life. The conditions which are 
favorable or unfavorable to health should be studied 
by each person for himself, so as to learn what condi- 
tions are necessary in order that he shall be kept in 
the best working condition. This, to a large extent, is a 
matter for individual investigation. Many problems 
arise also in each person's vocation which should be 
attacked by applying the scientific method. There- 
fore, we should encourage the child to look for prob- 
lems, to give attention to them when he sees them, and 
to be alive to the questions which may arise in connec- 
tion with his own life and with the world about him, 
in addition to training him in the ability to attack 
problems when they are pointed out. 

Exact generalization is induction. When generaliza- 
tion is carried to the point which has just been de- 
scribed, — that is, when it has been made definite and 



254 PSYCHOLOGY OF COMMON BRANCHES 

exact and has resulted from a scientific form of inquiry, 
— we call it "induction." Induction, then, is the 
examination of facts in a systematic fashion in order 
to determine from this investigation what general 
principles govern these facts. 

The formation of generalizations makes concepts 
more exact. In the foregoing description, scientific 
procedure has been described as the formation of 
generalizations. We may equally well describe it as 
the development of our ideas or our concepts. When 
the child learns about the habits of life of an animal, 
besides developing general principles as to the activi- 
ties of this animal, he is making fuller and more exact 
his concept or notion of what the animal is. In sim- 
ilar fashion, when the child is taught about the hea- 
venly bodies and learns the general principles which 
govern the movements of the moon and of the planets, 
and distinguishes the movements of these bodies from 
the comparative fixity of the stars, he is making more 
exact his conception of the meaning of star and planet 
and moon. 

Science also creates concepts. Scientific work, in 
fact, goes still beyond the process of rendering con- 
cepts more precise and exact. In its higher form it 
means the actual creation of new concepts to explain 
the facts as they are observed. Much of the science 
with which we are familiar uses ideas which could 
never arise from the sensations or perceptions we get 
from objects. We may think of our idea of a table, or 



NATURAL SCIENCE 255 

of a chair, or of a horse, as developing from the per- 
ception of a large number of these objects, and from 
our experience in using them, or in responding toward 
them. Such an idea as the atom, however, or of gravi- 
tation, or of ether vibrations, we would never get by 
such sensory experiences. These are creations of the 
imagination, which are brought into being to explain 
the events which we do observe in the physical world 
about us. 

This abstract form of science is beyond the compre- 
hension of the child below adolescence. Scientific 
investigation, and the thinking which results in the 
development of these more abstract forms of concept, 
represent a higher stage of development, both in the 
history of science and in the life of the child, than the 
simpler classifications and generalizations of those 
events which can readily be observed. They require a 
type of imagination which goes beneath the physical 
facts which impress the senses, and which is dependent 
on a larger amount of mental development than the 
young child is capable of. We may say in a general 
way that the science which has as its aim the explana- 
tion of physical facts by the creation of such concepts 
as these is beyond the child below the age of adoles- 
cence, and that only the simpler forms are usually 
grasped even at this age. 

Generalizations need to be tested. We have spoken 
of the development of scientific principles as though it 
consisted merely in generalization upon facts, and the 



256 PSYCHOLOGY OF COMMON BRANCHES 

form of intellectual procedure which has its culmina- 
tion in induction. There is another procedure which is 
continually used by scientific students, and which is 
important for all kinds of scientific procedure. One 
develops general principles, as has been said, by sys- 
tematically examining the facts and attempting to 
find a principle which will explain them. After this 
has been done, however, the generalization is not 
sufficiently certain until the principle which has thus 
been found is tested. 

Testing a proposed explanation is illustrated in the 
diagnosis of a pupil's poor work. This double proce- 
dure of seeking an explanation for observed facts and 
then testing the explanation may be illustrated from 
the experience of a teacher. The teacher discovers 
that a pupil is doing very poor work. He first casts 
about in his mind to find the explanation for this fact. 
He may examine the home life of the pupil to see if he 
has the proper surroundings and the proper encour- 
agement. He may consider the physical conditions of 
his life, the amount of his food, sleep, rest, and recrea- 
tion. He may consider his mental capacity and the 
question whether the work which is given to him is 
suited to his general ability, or to the special type 
of ability which he may possess. He may examine 
the pupil's interests and see whether he is distracted 
from his work by other and more powerful inter- 
ests. He may conclude, as a result of this examina- 
tion, that the pupil is doing poor work because the 



NATURAL SCIENCE 257 

work is not suited to his capacity. This, then, is a 
generaHzation. He may now test this generaUzation 
by changing the work in such a way that it will seem 
better suited to the pupil. If this results in improve- 
ment he may assume that the hypothesis which was 
laid down was at least in a measure correct. 

Another illustration may be found in the discovery 
of the planet Neptune. We may take as another illus- 
tration an example from the larger scientific world. 
We are all familiar with the law of gravitation. This 
is a generalization made upon a large number of occur- 
rences, such as the falling of bodies to the earth, the 
revolution of the moon about the earth and of the 
planets about the sun. The law of gravitation received 
a very remarkable confirmation through its application 
in one particular case. For a long time the movements 
of the planet Uranus were found not to be in accord- 
ance with the mathematical calculations of its course 
on the basis of the law of gravitation. Various theories 
were held to account for this, one of them being that 
the irregularities in movements were caused by the 
existence of another planet which had not yet been 
discovered. Two mathematicians worked out theo- 
retically the position and character of a planet which 
would account for these irregularities in movement. 
Astronomers then searched in the region of the sky 
at which such a planet should be located and discov- 
ered the existence of the planet Neptune. By this 
means the correctness of the theory was confirmed by 



258 PSYCHOLOGY OF COMMON BRANCHES 

the fact that the discovery of an object which previ- 
ously had not been known was predicted and then 
actually made. 

Deduction supplements induction. This mental 
process, by which we apply a general principle and 
work out its implication in the facts of the world about 
us, is called "deduction." These two forms of thinking 
are both important in scientific generalization. The 
one leads to the formations of generalizations; and the 
other to their testing, and to either their confirmation 
or rejection. 

Summary of the child's development in scientific 
thinking. Scientific thinking in its highest form may 
be seen, from the previous description, to be the refine- 
ment of forms of thinking which the child uses from 
the beginning. We must not think of the scientific 
method as something which is an entirely new devel- 
opment at a certain period in a child's life, and which 
amounts to a radical change or to the adoption of a 
new form of intellectual activity. From the earliest 
years the child begins to make generalizations, to 
form ideas, and to try out his generalizations by com- 
parison with the facts of his observation. As he grows 
older, he learns to observe in a more systematic 
fashion, and to experiment, in order that his generali- 
zations may be broader and more firmly founded. He 
learns to look for problems in the events which he has 
before taken for granted. As he grows still older, he 
sees still deeper problems and can appreciate the 



NATURAL SCIENCE 259 

search for concepts or ideas which will serve to illu- 
minate or explain them. He is still making generali- 
zations, he is still forming ideas, but they are of a more 
abstract character. He learns to see the connection of 
events which previously have had no connection with 
one another in his mind. He substitutes for the erro- 
neous conclusions, which have been created by popu- 
lar opinion to explain facts of experience, a more scien- 
tific and exact method. His development proceeds 
through the application of the general forms of think- 
ing which he has used right along, but the application 
of them becomes more regulariy arranged, follows 
better principles of procedure, and leads to more reli- 
able results. 

The practical and the theoretical in science teaching 

The child's interest develops from the practical to 
the theoretical. We have seen that the child's scien- 
tific interest grows out of the desire to generalize and 
to explain the facts of his experience. He is interested 
first in the more immediate problems, and his atten- 
tion is attracted to those situations which have a prac- 
tical meaning and which call for activity on his part. 
The interest in the generalizations of science is accom- 
panied by still stronger interest in the applications of 
these generalizations. The boy's interest in the theo- 
retical principles of physics is subordinate to his inter- 
est in wireless telegraphy or in X-rays; and the girl's 
interest in the principles of chemistry is less keen than 



260 PSYCHOLOGY OF COMMON BRANCHES 

her interest in the appHcation of these principles in 
cooking. 

The interest in practical applications is generally 
recognized. This interest which pupils manifest in the 
working of general scientific principles in the world 
about them is generally recognized by teachers of 
science in the elementary or the high school and by 
writers of textbooks for elementary or high-school 
pupils. A comparison of recent texts with those writ- 
ten less than a generation ago makes this clear. A 
glance at the illustrations of modern texts will show, 
besides the diagrams which give a graphic representa- 
tion of the abstract laws, and the cuts of laboratory 
apparatus, illustrations of engines and telephones; 
pictures of forests and lakes; of animals or articles of 
food. 

Science teaching may develop general principles 
from concrete problems or begin with general princi- 
ples and then proceed to apply them. While the use of 
a large amount of concrete material is a common 
feature of the prevailing methods of teaching, there is 
coming to be a sharp distinction in the way in which 
this concrete material is used. The customary method 
in the past has been to develop first the theoretical 
and abstract scientific principles and afterward make 
application of them to the practical concerns of every- 
day life. For example, the general principles of the 
mechanical effects of heat are first developed and 
they are then applied to explain the action of the 



NATURAL SCIENCE 261 

steam engine through the expansion of water under 
the influence of heat. 

Beginning with general principles means teaching 
the sciences separately. A consequence of this method 
is that the pupil is at first introduced to the highly 
differentiated branches of science. In the history of 
scientific development the tendency is toward a 
greater and greater splitting-up of the whole field, due 
largely to the interests of those who carry on advanced 
scientific investigation. When we teach pupils by 
beginning with the abstract, general principles, it is 
natural to treat the sciences according to the scheme 
of classification which has been gradually built up in 
the course of the development of science. The conse- 
quence of this mode of treatment is that the pupil is 
introduced immediately to highly abstract aspects of 
the physical world. 

Illustration of the opposite procedure. The effort is 
being made in many quarters to begin at the other 
end, by introducing the pupil first to typical problems 
as they arise in everyday life, and gradually develop- 
ing the abstract generalizations from these. To use 
the example which has already been cited, one would 
first, in following out this procedure, introduce the 
pupil directly to the study of engines, and out of this, 
and other similar cases, arrive at the general mechani- 
cal principles which serve to explain their action. 

Concrete situations usually involve several sciences. 
But there are other principles involved in the expla- 



262 PSYCHOLOGY OF COMMON BRANCHES 

nation of the engine than the mechanical principles of 
physics. Engines derive their energy from some form 
of combustion. In steam engines the combustion 
takes place outside the engine proper, while in gas 
engines it takes place within the engine; but in both 
cases the energy is released by changes in the composi- 
tion of the fuel. The explanation of this phase of the 
action of the engine requires the grasp of chemical 
principles. Again, if we investigate the sources of fuel 
energy, we are led to a study of the way in which com- 
plex chemical substances are built up in the growth of 
plants and stored in the wood of trees, or in the earth 
in coal or oil. In this study we get into the province of 
botany and even geology. 

Two methods of procedure in this case are open. If 
we begin with such concrete situations as this, two 
forms of procedure are open. On the one hand, a full 
explanation may be sought for all the problems which 
arise, and the search may be pushed into whatever 
field may need to be explored to reach the object; or, 
on the other hand, each practical situation may be 
used to illustrate only the general principle which is 
most prominently revealed in it, and the situations 
may be so selected as to illustrate a progressive and 
coherent group of principles. Even the second method 
would not involve the rigid separation of the principles 
of the various sciences, but would necessitate a con- 
tinuous intermingling and correlation. For example, 
to understand the flow of sap in a tree it is necessary 



NATURAL SCIENCE 263 

to have some grasp of the physical principle of capil- 
larity. 

The general principle is clear; the details remain 
to be worked out. Just how the relation between 
concrete situations and general scientific principles 
will be worked out in detail remains to be seen. This 
is a problem for the special workers in the field. A 
widely used text in general science, that by Caldwell 
and Eikenberry, makes the following division into 
large topics: (1) the Air; (2) Water and its Uses; 
(3) Work and Energy; (4) the Earth's Crust; (5) Life 
upon the Earth. Without committing ourselves to 
this or any particular choice of subjects, as a final list, 
it is clear that the general procedure which is here 
represented, of beginning with the objects of the pupil's 
environment and the problems which they present, 
and working from these concrete situations to the 
general principles which serve to explain them, is the 
procedure which is in accord with the development of 
the child's scientific thinking as it has been described 
in this chapter. It is also fairly clear that this involves 
some breaking-down of the rigid limits between the 
highly developed special sciences in the early stages 
of the student's scientific work. After he has attained 
some conception of the most important modes of the 
working of the physical world, he is ready to pursue 
the special laws of some particular class of facts in 
greater detail and with greater precision, and to follow 
some of the more abstract theories and speculations. 



QUESTIONS AND TOPICS FOR 
DISCUSSION 

CHAPTER I 

1. Show that the different school subjects require of the child dif- 
ferent kinds of learning. Think out illustrations of your own. 

2. Can you give any evidence that learning, if it is properly super- 
vised and directed, may be made more economical than it would 
otherwise be? 

3. Support by any argument yon can the view that a knowledge 
of the learning process is of value to the teacher. 

4. Why is the teacher's childhood experience in the school not 
sufficient to give this knowledge? 

CHAPTER II 

1. Give all the illustrations you can of motor habits which are 
trained in the school. 

2. Compare the complexity of the writing movement with the 
walking movement. Why does the child take longer to learn to 
write than to walk? 

3. What conditions determine the slant of writing? 

4. If the same conditions operated, what would be the slant in left- 
hand writing? 

6. What important change in the method of writing has been made 
in order to conform to the demands of hygiene? How have 
these demands been met subsequently in a different way? 

6. Does "selection" of appropriate movements mean conscious, 
deliberate selection? If not, what is the method? 

7. Give illustrations of inhibition in other kinds of behavior, such 
as thinking. 

8. Illustrate the value of rhythm. 

9. Discuss the saying, "Practice makes perfect." 

10. What changes in writing accompany the automatization of the 
movement? 

11. Discuss the statement, "If the child is trained in the correct 
movement, the form of the letters will take care of itself." 



266 QUESTIONS AND TOPICS FOR DISCUSSION 

12. Compare two methods of stimulating the child to a study of the 
form of his writing. 

13. Illustrate good form in other movements than writing. 

14. Compare the two methods of grading the child's work. 

15. Why should the correct habit be practiced in all writing? Put 
this rule in the form of a general principle and illustrate from 
other subjects of study. 

16. Compare the movements made by a child of three years and of a 
child of eight or nine and inquire whether the fundamental and 
accessory theory explains the difference. 

17. Considering the motor development of the child and the need of 
making writing automatic, when do you think writing drill 
should be emphasized most? 

18. Discuss the aim of bringing all the children of a grade up to a 
grade standard and giving none drill who are above this stand- 
ard. 

CHAPTER m 

1. Is perceptual learning well described as the acquisition of knowl- 
edge? Compare it with learning the facts of history or geo- 
graphy. 

2. Give other illustrations to show that perception is not a matter 
of passively gaining impressions. 

3. Look up other definitions of apperception. Is there any reason 
for retaining the term? 

4. What is necessary, besides the presentation of an object to the 
senses, for the success of object teaching? 

5. How are recognition and appreciation related to expression, as 
illustrated by drawing? 

6. On what fact does th^ difficulty in representing perspective rest? 

7. Is the nature of the child's early drawing due solely to his in- 
ability to master technical difficulties? 

8. Gather or observe some drawings of young children and show 
what is meant by describing them as symbolic. 

9. Compare diagramming with the child's early drawing. 

10. Does interpretation as a feature of perception mean the same as 
the interpretation of a poem? 

11. If you have opportunity, practice with some illusion until it is 
overcome or reduced in amount. The Poggendorf illusion, or the 
illusion of the circles, mentioned in chapter i of Judd's Gcnelic 
Psychology for Teachers, are good ones to use. 

12. What is the chief motive for improvement in perception? What 
is the place of formal training in sensory discrimination? 



QUESTIONS AND TOPICS FOR DISCUSSION 267 

13. If it is available, consult Winch's Children's Perceptions (War- 
wick and York, Baltimore) and 6nd illustrations of any princi- 
ples of this chapter. 

14. Why is sense training to be distinguished from perceptual train- 
ing? 

15. Get some facts, if you can, to show the need of diagnosing and 
correcting sensory defects. 

CHAPTER IV 

1. Compare formal drill and the expression or the recognition of 
meaning in both reading and writing. 

2. Should formal drill precede, accompany, or follow the recogni- 
tion of meaning? 

3. Is the statement, "The letters need not be learned first," equiv- 
alent to saying, "The letters need not be learned"? Why? 

4. Is learning to say over the alphabet what is meant by learning 
the letters, in question 3 ? 

5. Compare the child's progress in learning to recognize a word with 
the process in learning the figure in chapter iii. 

6. Mention three stages in the development of the alphabet. 

7. Find an illustration of phonetic drill in a first-grade reader and 
describe it. 

8. Why is the incidental method uneconomical when used alone? 

9. Compare the type of eye movement in reading with other types 
of movement you may be able to observe. Is the reading habit 
found anywhere else? 

10. What other activities correspond to the reading of the sentence 
as a whole? 

11. Why do you think oral reading has been so prominent in the 
school? 

12. Is oral reading of equal value in different stages of the child's 
development? Why? 

13. Measure your rate of reading and your ability to reproduce 
what is read when reading carefully, at ordinary speed, and 
rapidly. Try the experiment with different kinds of subject- 
matter. Do your results agree with the conclusions of the 
chapter? 

14. In what chiefly do the upper grades excel the lower ones in 
reading? 

15. How are the mechanics of reading developed? 



268 QUESTIONS AND TOPICS FOR DISCUSSION 



CHAPTER V 

1. Supplement the discussion in the book by suggesting a method 
of teaching the child to sing from ear. 

2. Test the ability of several people, first, in the recognition of 
absolute pitch, and, second, in the recognition of intervals. 
Compare the amount of error in the two cases. 

3. Similarly, test the ability of several persons to strike a single 
note or an interval from the printed score, and compare the 
errors. 

4. Is the discrimination between the whole and the half steps on 
the musical scale a clearly recognized matter in the mind of the 
person who has not had special musical training? 

5. Can you show that, while the recognition of difi'erences in inter- 
vals may not be explicit, the untrained person nevertheless uses 
the conventional scale as the basis of his recognition of musical 
melody? 

6. What analogy is there in another form of learning already stud- 
ied to the practice of deferring formal instruction in the scale 
imtil the child has gained some reading ability? 

7. What is the chief difficulty incident to the use of different keys? 

8. Is formal instruction in scales and keys desirable? Why? 

9. Name all the cases of rhythmical involuntary activities you can. 
What inference is suggested? 

10. What is there in the appreciation of rhythm in music besides 
the mere understanding of the meaning of musical notation? 

11. Is there a sharp distinction between harmony and disharmony? 

12. Why is tone quality not one of the chief objects of musical train- 
ing in the school? 

13. If a child cannot distinguish the pitch of middle C and C sharp, 
what would you advise regarding his musical training? How 
would you determine his ability in pitch discrimination? 

CHAPTER VI 

1. May inaccurate spelling be adequate for reading and not for 
writing? Illustrate. 

2. What are the movements which may be associated in spelling? 

3. Why must learning to spell English words be in a measure 
arbitrary? 

4. Examine the words in some spelling book, — or better, two 
spelling books, an older one and a recent one, — and estimate 
the proportion of the words that are in common use in the writ- 
ing of the average person. 



QUESTIONS AND TOPICS FOR DISCUSSION 269 

5. Why should the child, so far as possible, learn to spell by sound, 
analogy or rules? 

6. Why were the inferences from the Philadelphia investigation 
not conclusive? 

7. Compare the essential principles of drill in spelling and in writing. 

8. Cite any illustrations you can of children's enjoyment of drill. 

9. Why is a variety of modes of presentation best? 

CHAPTER VII 

1. Show some of the ways in which the child's imagination is 
stimulated before he enters school. When does imagination 
develop? 

2. Compare memory and imagination. 

3. Illustrate further verbal imagination. 

4. Investigate differences in imagery among persons of your ac- 
quaintance, and report. 

5. Is it correct to say that the child is more imaginative than the 
adult? Amplify your answer. 

6. Is biography history? 

7. How do you think of events at different past and future dates? 
How is the time represented in your mind? 

8. Make an experiment upon the time sense of another person by 
asking him to estimate an interval when he does not know, and 
another when he does know, that you are observing him. 

9. Describe your notion of the following time periods: second, 
minute, hour, day, week, month, year, century. 

10. What does simplicity in early history mean? 

11. Make a brief outline of beginning history that would conform 
to the principles laid down in the chapter. 

12. Illustrate methods of developing the simpler form of the his- 
torical sense. 

13. How is tolerance, historical or otherwise, developed? 

14. Is the higher form of the historical sense connected with the 
grasp of historical development? 

15. Illustrate helpful and futile use of sources with high-school 
pupils. 

CHAPTER VIII 

1. Can you show that the understanding of physical and commer- 
cial geography is dependent upon a knowledge of place geo- 
graphy? 

2. What is the practical application of the fact that localization of 
places is the outgrowth of the sense of bodily position? 



270 QUESTIONS AND TOPICS FOR DISCUSSION 

3. Relate any case of false orientation you have experienced and 
interpret your experience. Did false orientation have to be 
readjusted piecemeal? 

4. Compare cases in which your sense of direction was good with 
cases in which it was poor, and explain the difference. 

5. How may the gap between experience with a narrow range of 
objects and the notion of a broad region be bridged? 

6. If maps are used abstractly by adults, why need we try to give 
them concrete meaning to the child? 

7. Outline briefly some lessons in home geography to show their 
general nature. 

CHAPTER IX 

1. Make a list of other abstract ideas besides number, — if neces- 
sary, after the consultation of a textbook on psychology, — and 
point out their common feature. 

2. Mention other illustrations of objects used as counters. 

3. If symbols imply the abstractness of an idea, have we met any 
abstract ideas in connection with the subjects previously dis- 
cussed? In what way is number more abstract than these? 

4. Show the importance of counting in the child's early number 
development. 

6. Use X and y as number symbols for 10 and 11 in order to carry 
the unit group to 12 instead of 10; turn the numbers 47 and 58 
into terms of this notation. Turn the numbers 12 and 23 into 
the new notation; multiply and turn the answer into ordinary 
symbols to prove. 

6. Illustrate the multiplication of 4 by 5 by using the two types of 
concrete experience, measurement, and grouping. 

7. Illustrate the number 23 by groups of dots. 

8. How far do you think it is possible to go in leading the child to 
an understanding of the number symbols and processes? 

9. Mention several forms of number drill. 

10. What are the reasons for treating addition and multiplication 
before subtraction and division? Is the implication that the 
study of the first two should be completed before the second 
two are studied? 

11. What is a fraction? 

12. Why are percentages more easily manipulated than other frac- 
tions? 

13. What is the essential difference between algebra and arithmetic? 

14. State and illustrate some of the processes which can be em- 
ployed to modify the form of an equation. 



QUESTIONS AND TOPICS FOR DISCUSSION 271 

15. Make the following equation concrete by substituting for the 
algebraic symbols numerical terms and show that the equation 
(x-\-y) {x—ij) = x^ — y^ holds true. 

16. Illustrate a method by which the child may be led to recognize 
through concrete experience what is the sum of the angles of a 
triangle and of a quadrilateral. 

17. How might the relation of the length of the diameter to the 
circumference of a circle be approximately determined by a 
concrete method? 

18. Compare the stages in the solution of an original problem in 
geometry with the stages in the reasoning problems given by 
Dewey in How We Think, chapter VI. 

19. Apply to some other field the distinction between problem 
solving and following another's demonstration. 

20. Look up some problem in arithmetic, and distinguish between 
the understanding of the conditions of the problem and of the 
mathematical process used in solving it. 

CHAPTER X 

1. Give three scientific generalizations and three generalizations in 
other fields. 

2. Mention other expectations which the child forms and which 
imply some generalization upon his experience without an 
explicit formulation. 

S. Collect and compare definitions from children of different ages, 
or find instances in child-study literature. 

4. Can you show the effect of names in stimulating concept forma- 
tion from your experience in this course.' 

5. Compare your explanation of some fact in a field in which you 
have studied with the explanation you can give of a fact in an 
unfamiliar field. 

6. State some popular beliefs which rest on superficial observation. 

7. Give one other illustration than those given in the book of the 
light thrown by scientific study upon the affairs of everyday life. 

8. How much original investigation of a scientific sort do you 
think the child can do independently? Is there any intermediate 
type of investigation between independent research and learning 
from others? 

9. Give an illustration of your own of experimentation. 

10. Show that induction and deduction may be used in the investi- 
gation of some practical problem. 

11. Is it correct to say that the child has no theoretical interest? 

12. Do you think the natural order is from the theoretical interest 
to the practical application or the reverse? 



INDEX 



Abacus. 196. 

Absolute pitch, 100. 

Abstract ideas, 150, 173, 179 

/.. 221. 
Accessory movement, deBned, 

30. 
Activity in learning, 36, 45. 
Addition, 201 /., 218. 
Age, changes with, 29 ff., 43, 46, 

59, 95, 112 /., 141 /., 145 /., 

156, 159, 242/., 255. 
Algebra, 209 /. 
Alphabet, 74 f. 
Angell, J. R., 160. 
Apperception, 40; defined, 42. 
Application in science teaching, 

260 Jf. 
Arithmetic, 183/. 
Arm position in writing, 11. 
Association, 116/., 127. 
Attention in learning, 126. 
Automatic activity, defined, 22. 
Automatization, 18, 22. 
Ayer, F. C, 49. 
Ayers, L. P., 33, 131. 

Barnes, E., 66. 
Binet, A., 145, 178. 
Biography, 144. 
Bourne, H. E., 160. 

Caldwell, O. W., 263. 
Cardinal number, 187. 
Cardinal points, 165, 167/., 176. 
Causes in science, 251 /. 
Chinnappa, S. P., 47. 
Clark, A. B., 66. 
Cleveland, spelling in, 125, 128/. 
Conant, L. L., 186. 
Concept, 241 /., 254. 



Concrete experience, 150, 173, 

191, 217, 224, 234, 260. 
Congdon, C. H., 105, 114. 
Copy in handwriting, 24. 
Cornman, O. P., 124, 131. 
Counting, 182. 
Courtis, S. A., 234, 237. * 
Cowling, D. J., 66. 

Dancing, 107. 

Dearborn, W. F., 93, 97. 

Decimal system, 189, 193, 207. 

Deduction, 258. 

Definitions, child's early, 5i42. 

Dewey, J., 238. 

Diacritical marks, 80. 

Diagramming, 48. 

Diffusion in learning, 13. 

Digits, 186. 

Discrimination, 57, 64, 112. 

Division, 201 /. 

Double images, 55. 

Drawing, analysis of, 34/., 42/. 

Drill, 68, 78, 96, 122/., 200. 

Eikenberry, W. L., 263. 

Equation, 213/. 

Euclid, 223. 

Excursions, 177. 

Experimentation, 249/. 

Eye adjustments in writing, 10. 

Eye movements in reading, 82. 

Farnsworth, C. H., 114. 
Feebleminded child, 65. 
Form of letters in writing, 20, 24/. 
Fractions, 205 /. 
Freeman, 25, 33, 237. 
Fundamental and accessory 
movements, 29. 



274 



INDEX 



Fundamental movement, de- 
6ned, 30. 

Fundamental operations in arith- 
metic, 194, 201 /. 

General ideas, 37. 

Generalization, 227 /., 245, 255; 
deBned, 240. 

Geography, physical and com- 
mercial, 161 /. 

Geometry, 222/, 

Globes, 171 /. 

Good form in learning, 26. 

Grouping in number, 187, 189 /., 
193 /., 205 /., 208. 

Habit, 6, 28. 
Hall, G. Stanley, 63, 66. 
Halleck, R. P., 62, 66. 
Handwriting, speed, 19, 26. 
Handwriting and spelling, 115, 

118. 
Handwriting movement, 7, 25. 
Harmony, musical, 109/. 
Hicks, Warren E., 125. 
Historical development, grasp 

of, 157. 
Historical sense, 153 ff. 
Home geography, 173 Jf . 
Huey, E. B., 75/., 97. 

Illusion, defined, 54. 
Imagination, 132 jf., 140, 161/.; 

defined, 133, 140. 
Incidental method, 78, 122. 
Individual differences, 32, 60, 

110, 112/., 137. 
Induction, 253. 
Inhibition, 13. 

Inner speech in reading, 85 /. 
Intervals in pitch, recognition 

of, 100. 

Jenkins, F., 97. 
Jones, W. F., 131. 
Judd, Charles H., 33, 66. 77, 97, 
178, 194, 237. 

Keys, musical, 103/. 
Kirkpatrick, E. A., 57. 



Language, 135, 140, 243. 
Lloyd, Sam, 215. 
Lukens, H. T., 66. 

McClellan, J. A., 238. 
Maps, 171 /. 
Meanings, 22. 58, 67 /. ' 
Measurement, 195, 222/. 
Mechanical drawing, 48. 
Melody, 100/. 
Memorizing, 115, 134, 138. 
Monroe, W. S., 238. 
Motor coordination, 15. 
Multiplication, 201/., 220/. 
Myers, G. W., 220. 

Names, 243. 

Natural science, 162, 239/, 
Negative numbers, 218. 
Neighborhood history, 152/. 
Neptune, discovery of, 257. 
Notation, musical, 101, 104, 108. 
Notation, number, 190, 207. 
Number, 149 /., 179 /., 251. 
Number names, 182/., 186. 

Object in perception, 55. 
Object teaching, 40. 
Observation, 59, 249 /. 
One-to-one correspondence, 183. 
Oral expression, 70. 
Oral reading, 86 /. 
Ordinal number, 187. 
Orientation, 163/.; defined, 164. 

Percentage, 207. 
Perception, 51/., 116. 
Perceptual learning, 36/. 
Perspective, 43. 

Philadelphia, spelling in, 124 /. 
Phonetics, 73/., 79, 119/. 
Picture writing, 75. 
Posture in writing, 11. 
Practice periods, 33. 
Presentation, method of, 129 /. 
Preyer, S. 243. 

Principles, general, 241 /., 260. 
Problem solving, 229/., 252, 
Pronation, 9, 



INDEX 



275 



Proof. 228 /. 

Pythagorean theorem, 225 f. 

Quality in handwriting, 26. 
Quantity, 185. 

Ratio, 204 /., 213. 
Reading efficiency, 89 ff. 
Reading and spelling, 118. 
Repetition in learning, 17, 126. 
Rhythm, 16, 18, 106/. 
Rice, J. M., 123/., 131, 
Rowe, S. H., 33. 

Sargent, Walter, 45, 66. 
Scale, musical, 101 /. 
Scope of attention, 188 /. 
Seashore, C. E., 112/., 114. 
Selection in learning, 12. 
Sensation, 51, 134. 
Sense training, 61 ff. 
Sensori-motor activity, 6. 
Sensori-motor coordination, 8, 

15. 
Sensory defects, 64. 
Sentence reading, 73, 84. 
Silent reading, 86 ff. 
Singing by ear, 98 /. 
Slant in writing, 9. 
Smith, D. E., 210, 238. 
Sound localization, 56. 
Sources in history, study of, 

158/. 



Spatial imagination, 153, 169 /. 

Spelling in reading, 81. 

Spencer, H., 238. 

Stimulus, 6. 

Subtraction, 201/., 218/. 

Suggestibility, 59. 

Suzzalo, H., 131. 

Symbolism in early drawing, 47. 

Symbols, 75, 182/., 196, 211/. 

Taylor, I., 77. 

Temporal imagination, 145/. 

Thorndike, E. L., 33. 

Time sense, 146. 

Tolerance, attitude of, 155/. 

Tone quality. 111. 

Transfer of training, 128. 

Trial and success (trial and error) 

method, defined, 17. 
Types, mental, 60. 

Uniformity in writing, 20. 

Unit, 184/., 190. 
Uranus, planet of, 257. 

Waldo, K. D., 90, 96, 97. 
Wallin, J. E. W., 124/., 131. 
Whitehouse, W. A., 26, 33. 
Word learning, 71. 

Young, J. W. A., 238. 

Zook, S. A., 127. 








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